Here is a comparison of the running times between the current LREtools[hypergeomsols] and my new implementation. ------------------------------------------- Example | Maple6 | new code | speedup | CPU time | CPU time | factor | | | number 1, 0.230, 0.170, 1.35 number 2, 0.860, 0.370, 2.32 number 3, 0.090, 0.200, 0.45 number 4, 3.310, 0.630, 5.25 number 5, 1.420, 0.320, 4.44 number 6, 1.300, 0.380, 3.42 number 7, 8.520, 0.580, 14.69 number 8, 0.580, 0.310, 1.87 number 9, 0.230, 0.200, 1.15 number 10, 0.270, 0.450, 0.60 number 11, 0.060, 0.010, 6.00 number 12, 9.610, 0.920, 10.45 number 13, 2.480, 0.430, 5.77 number 14, 0.030, 0.140, 0.21 number 15, 78.160, 2.610, 29.95 number 16, 292.510, 0.660, 443.20 number 17, 0.400, 0.270, 1.48 number 18, 0.200, 0.210, 0.95 number 19, 18.540, 1.110, 16.70 number 20, 33.220, 1.730, 19.20 number 21, 6.180, 0.330, 18.73 number 22, 0.110, 0.020, 5.50 number 23, 12.950, 0.860, 15.06 number 24, 12.780, 1.000, 12.78 number 25, 1.800, 0.400, 4.50 number 26, 255.090, 2.660, 95.90 number 27, 13.910, 1.490, 9.34 number 28, 3378.200, 6.080, 555.62 number 29, 258.540, 5.460, 47.35 number 30, out of memory, 19.100, infinity number 31, 0.500, 0.340, 1.47 number 32, 4.620, 0.540, 8.56 number 33, 4.600, 1.230, 3.74 number 34, 0.700, 0.340, 2.06 number 35, 5.480, 0.050, 109.60 number 36, 1.480, 0.550, 2.69 In 4 out of 36 examples the current Maple6 code was faster. In 18 out of 36 examples the speedup factor was between 1 and 10. In 14 out of 36 examples the speedup factor was > 10. In 4 out of 36 examples the speedup factor was > 100. Remark 1: In the examples where the current Maple6 code was faster, the CPU time is very small for both, and so the difference is very small as well (0.11, 0.18, 0.11, and 0.01 seconds). Remark 2: For fair comparison, the test examples were not chosen by me but were sent to me by Ha Le. Remark 3: My own test examples are generally more complicated, which makes the difference bigger (i.e. most of these examples are too hard for the current Maple6 code, but run without troubles with the new code). Mark ---------- Test examples -------------------- rec_p[1]:=(2+3*n+n^2)*v(n)+((-2*a+1+a^2)*n^2+(-6*a+3+3*a^2)*n-4*a+2+2*a^2)*v(n+2)+ ((-2+2*a)*n^2+(6*a-6)*n+4*a-4)*v(n+1): rec_p[2]:=(2+5*n+2*n^2)*v(n)+((4*a-2)*n^2+(-5+11*a)*n+7*a-3)*v(n+1)+((-2*a+2*a^2)*n^2+ (6*a^2-6*a)*n+4*a^2-4*a)*v(n+2): rec_p[3]:=(-1-n^2-2*n)*v(n+1)+((3-a)*n^2+(-3*a+9)*n-2*a+6)*v(n+2): rec_p[4]:=(-2-5*n-2*n^2)*v(n)+(2*n^3+(13-4*a)*n^2+(-11*a+23)*n+12-7*a)*v(n+1)+ ((4*a-2)*n^3+(-2*a^2+25*a-11)*n^2+(-6*a^2+47*a-19)*n-4*a^2+26*a-10)*v(n+2)+ ((-2*a+2*a^2)*n^3+(-12*a+12*a^2)*n^2+(-22*a+22*a^2)*n-12*a+12*a^2)*v(n+3): rec_p[5]:=(54+99*n+54*n^2+9*n^3)*v(n)+((-6+27*a)*n^3+(162*a-36)*n^2+(-66+297*a)*n+ 162*a-36)*v(n+1)+((-12*a+27*a^2+1)*n^3+(162*a^2+6-72*a)*n^2+(297*a^2+11-132*a)*n+ 162*a^2+6-72*a)*v(n+2)+((a-6*a^2+9*a^3)*n^3+(-36*a^2+6*a+54*a^3)*n^2+(11*a-66*a^2+ 99*a^3)*n-36*a^2+6*a+54*a^3)*v(n+3): rec_p[6]:=(-2+n^2-n)*v(n)+((2*a+1)*n^2+(2*a+2)*n+1)*v(n+1)+((a+a^2)*n^2+(3*a+3*a^2)*n+ 2*a+2*a^2)*v(n+2): rec_p[7]:=(60+141*n+108*n^2+27*n^3)*v(n)+((-4+81*a)*n^3+(378*a-26)*n^2+(573*a-52)*n+ 276*a-30)*v(n+1)+((-8*a+81*a^2)*n^3+(432*a^2-50*a)*n^2+(729*a^2-94*a)*n+378*a^2- 52*a)*v(n+2)+((-4*a^2+27*a^3)*n^3+(162*a^3-24*a^2)*n^2+(297*a^3-44*a^2)*n+162*a^3- 24*a^2)*v(n+3): rec_p[8]:=(n^2+2*n+1)*v(n)+((2*a+1)*n^2+(2+5*a)*n+1+3*a)*v(n+1)+((a+a^2)*n^2+(3*a+ 3*a^2)*n+2*a+2*a^2)*v(n+2): rec_p[9]:=(-1+2*n+n^2)*v(n)+((2*a+1)*n^2+(3+5*a)*n+2+3*a)*v(n+1)+((a+a^2)*n^2+(3*a+ 3*a^2)*n+2*a+2*a^2)*v(n+2): rec_p[10]:=(35+12*n+n^2)*v(n)+((2*a-1)*n^2+(15*a-7)*n+13*a-6)*v(n+1)+((a^2-a)*n^2+ (3*a^2-3*a)*n-2*a+2*a^2)*v(n+2): rec_p[11]:=(n+1)*v(n+1): rec_p[12]:=(n-3)*v(n-1)+(-2*a+2*n*a)*v(n)+(n^3-2*n^2+(a^2-1)*n+2+a^2)*v(n+1)+(4*n^2*a- 2*n*a-4*a+2*n^3*a)*v(n+2)+((2+a^2)*n^3+(12+6*a^2)*n^2+(22+11*a^2)*n+12+6*a^2)*v(n+3): rec_p[13]:=(9*n-3*n^2)*v(n)+((-6*a-2)*n^2+6*a+2)*v(n+1)+((-2*a-3*a^2)*n^2+(-9*a^2- 6*a)*n-6*a^2-4*a)*v(n+2): rec_p[14]:=(11*n+6+n^3+6*n^2)*v(n+2)+((a-1)*n^3+(6*a-6)*n^2+(11*a-11)*n+6*a-6)*v(n+3): rec_p[15]:=(20-9*n+n^2)*v(n-6)+(112*a-60*n*a+8*n^2*a)*v(n-5)+((-4+28*a^2)*n^2+(-168*a^2+ 12)*n+254*a^2-2)*v(n-4)+((56*a^3-24*a)*n^2+(48*a-252*a^3)*n+292*a^3)*v(n-3)+((-2- 60*a^2+70*a^4)*n^2+(-210*a^4+6+60*a^2)*n+170*a^4-22+12*a^2)*v(n-2)+((-8*a-80*a^3+ 56*a^5)*n^2+(12*a-84*a^5)*n+8*a^3-40*a+40*a^5)*v(n-1)+((-12*a^2-60*a^4+28*a^6+4)*n^2+ (-12-60*a^4)*n-18*a^2+2-18*a^4+2*a^6)*v(n)+((8*a-24*a^5+8*a^7-8*a^3)*n^2+(12*a^7-48*a^5- 12*a^3)*n-24*a^5-8*a+4*a^7-4*a^3)*v(n+1)+((-4*a^6+1+a^8-2*a^4+4*a^2)*n^2+(3*a^8-12*a^6+ 3+12*a^2-6*a^4)*n-8*a^6+2*a^8+8*a^2-4*a^4+2)*v(n+2): rec_p[16]:=(-2+5*n+4*n^2+n^3)*v(n)+((-2+3*a)*n^3+(-15+14*a)*n^2+(21*a-26)*n+10*a-13)*v(n+1)+ ((-4*a+3*a^2+1)*n^3+(11+16*a^2-27*a)*n^2+(-53*a+26+27*a^2)*n-30*a+14*a^2+16)*v(n+2)+ ((a-2*a^2+a^3)*n^3+(6*a-12*a^2+6*a^3)*n^2+(11*a+11*a^3-22*a^2)*n+6*a-12*a^2+6*a^3)*v(n+3): rec_p[17]:=(-a^2+4+4*n^2)*v(n)+(4*a^2*n^2+12*a^2*n+8*a^2)*v(n+2)+(12*n*a+4*a+8*n^2*a)*v(n+1)- 2*v(n-1)*a-v(n-2): rec_p[18]:=v(n-1)+(a+1+n^2)*v(n)+((2*a+4)*n^2+(3*a+3)*n+a-1)*v(n+1)+((4*a+a^2)*n^2+ (12*a+3*a^2)*n+8*a+2*a^2)*v(n+2)+(11*n+6+n^3+6*n^2)*v(n+3): rec_p[19]:=(2*n^3+6*n-7*n^2)*v(n-1)+((8*a-2)*n^3+(-9*a+5)*n^2+(-a+2)*n+a-5)*v(n)+ ((12*a^2-6*a)*n^3+(-2*a+15*a^2)*n^2+(2*a^2+9*a)*n+5*a-a^2)*v(n+1)+((8*a^3-6*a^2)*n^3+ (-19*a^2+29*a^3)*n^2+(31*a^3-15*a^2)*n+10*a^3-2*a^2)*v(n+2)+((2*a^4-2*a^3)*n^3+(12*a^4- 12*a^3)*n^2+(22*a^4-22*a^3)*n+12*a^4-12*a^3)*v(n+3): rec_p[20]:=(-72-n^4+132*n+15*n^3-74*n^2)*v(n-2)+(-216*n^2*a+65*n^3*a+229*n*a-6*a*n^4- 72*a)*v(n-1)+(-15*n^4*a^2+(-1+100*a^2)*n^3+(14-159*a^2)*n^2+(-65+20*a^2)*n+100)*v(n)+ (-20*a^3*n^4+(-3*a+50*a^3)*n^3+(44*a^3+22*a)*n^2+(-44*a^3-27*a)*n-52*a-18*a^3)*v(n+1)+ (-15*a^4*n^4+(-25*a^4-3*a^2)*n^3+(36*a^4+2*a^2)*n^2+(27*a^2+58*a^4)*n+12*a^4+ 22*a^2)*v(n+2)+(-6*a^5*n^4+(-a^3-35*a^5)*n^3+(-6*a^3-60*a^5)*n^2+(-11*a^3-25*a^5)*n+ 6*a^5-6*a^3)*v(n+3)+(-35*n^2*a^6-24*a^6-50*n*a^6-10*a^6*n^3-a^6*n^4)*v(n+4): rec_p[21]:=(-2*n^4-100*n-20*n^3-70*n^2-48)*v(n)+((-8*a+1)*n^4+(10-80*a)*n^3+(35- 280*a)*n^2+(-400*a+50)*n-192*a+24)*v(n+1)+((1-12*a^2+3*a)*n^4+(-120*a^2+30*a+10)*n^3+ (35+105*a-420*a^2)*n^2+(150*a-600*a^2+50)*n+24+72*a-288*a^2)*v(n+2)+((2*a-8*a^3+ 3*a^2)*n^4+(30*a^2+20*a-80*a^3)*n^3+(-280*a^3+70*a+105*a^2)*n^2+(-400*a^3+150*a^2+ 100*a)*n+72*a^2-192*a^3+48*a)*v(n+3)+((-2*a^4+a^2+a^3)*n^4+(10*a^2-20*a^4+10*a^3)*n^3+ (-70*a^4+35*a^2+35*a^3)*n^2+(-100*a^4+50*a^3+50*a^2)*n-48*a^4+24*a^3+24*a^2)*v(n+4): rec_p[22]:=(a-1)*v(n)+(2+3*n+n^2)*v(n+2)+v(n-1): rec_p[23]:=(n-3)*v(n-1)+(-2*a+2*n*a)*v(n)+(n^3-2*n^2+(a^2-1)*n+2+a^2)*v(n+1)+(4*n^2*a- 2*n*a-4*a+2*n^3*a)*v(n+2)+((2+a^2)*n^3+(12+6*a^2)*n^2+(22+11*a^2)*n+12+6*a^2)*v(n+3): rec_p[24]:=(n-3)*v(n-1)+(-2*a+2*n*a)*v(n)+(-n^3+2*n^2+(a^2+1)*n+a^2-2)*v(n+1)+(2*n*a- 4*n^2*a-2*n^3*a+4*a)*v(n+2)+((-a^2+2)*n^3+(-6*a^2+12)*n^2+(-11*a^2+22)*n-6*a^2+12)*v(n+3): rec_p[25]:=v(n)*n^2+(3*n*a+a+2*n^2*a)*v(n+1)+((a^2-1)*n^2+(-3+3*a^2)*n-2+2*a^2)*v(n+2): rec_p[26]:=v(n-1)+(a-1)*v(n)+(2-n^3-2*n^2+n)*v(n+2)+(-n^4+(-5-a)*n^3+(-5-6*a)*n^2+(5- 11*a)*n-6*a+6)*v(n+3)+((-a+1)*n^4+(-10*a+10)*n^3+(-35*a+35)*n^2+(-50*a+50)*n-24*a+ 24)*v(n+4)+(-225*n^2-274*n-n^5-15*n^4-120-85*n^3)*v(n+5)+(20*n^6+140*n^2+889*n^3-720+ 560*n^4+154*n^5-1044*n+n^7)*v(n+6)+((a-1)*n^7+(28*a-28)*n^6+(-322+322*a)*n^5+(1960*a- 1960)*n^4+(6769*a-6769)*n^3+(-13132+13132*a)*n^2+(13068*a-13068)*n-5040+5040*a)*v(n+7)+ (870*n^7+9450*n^6+63273*n^5+269325*n^4+723680*n^3+1172700*n^2+1026576*n+362880+n^9+ 45*n^8)*v(n+9): rec_p[27]:=(n-5)*v(n-4)+(5*n*a-19*a)*v(n-3)+((-2+10*a^2)*n+6-26*a^2)*v(n-2)+((-1+10*a^3- 6*a)*n+10*a-1-14*a^3)*v(n-1)+((-2*a+1+5*a^4-6*a^2)*n-a^4-2*a-1+2*a^2)*v(n)+((-a^2+a+1+ a^5-2*a^3)*n-a^2+a+1+a^5-2*a^3)*v(n+1): rec_p[28]:=(n-7)*v(n-5)+((6*a-6)*n+36-34*a)*v(n-4)+(n^3-14*n^2+(76-30*a+15*a^2)*n-155- 65*a^2+138*a)*v(n-3)+((-5+6*a)*n^3+(-64*a+52)*n^2+(-60*a^2-179+20*a^3+266*a)*n-402*a+ 204+192*a^2-60*a^3)*v(n-2)+((15*a^2-25*a+10)*n^3+(-110*a^2+178*a-66)*n^2+(-401*a+ 15*a^4-60*a^3+138+315*a^2)*n-90+276*a-25*a^4+108*a^3-298*a^2)*v(n-1)+(n^5-15*n^4+ (20*a^3-50*a^2+40*a+61)*n^3+(-138*a-80*a^3-109+192*a^2)*n^2+(70-30*a^4+6*a^5-184*a^2+ 120*a^3+118*a)*n-2*a^5+16+14*a^2-8*a-26*a^3+12*a^4)*v(n)+((5*a-5)*n^5+(-45*a+45)*n^4+ (-69-50*a^3+60*a^2+53*a+15*a^4)*n^3+(13*a-18*a^2+28*a^3-10*a^4-25)*n^2+(74+64*a^3- 6*a^5-68*a^2-82*a+a^6-10*a^4)*n-14*a^3+10*a^2+15*a^4+8*a-20-6*a^5+a^6)*v(n+1)+((10+ 10*a^2-20*a)*n^5+(-30-30*a^2+60*a)*n^4+(40*a^3+212*a-122*a^2-86-25*a^4+6*a^5)*n^3+ (-22*a^2+114*a^3+16*a^5+102-68*a^4-64*a)*n^2+(28*a^2+148+6*a^5+62*a^3-156*a-29*a^4)*n- 12*a^3+40*a-32*a^2-4*a^5+14*a^4)*v(n+2)+((-30*a^2+30*a-14+10*a^3)*n^5+(-90*a^2-42+ 90*a+30*a^3)*n^4+(206*a^2+a^6-5*a^5-74*a^3+10*a^4-186*a+82)*n^3+(-666*a-294*a^3- 30*a^5+786*a^2+6*a^6+60*a^4+282)*n^2+(110*a^4-55*a^5+11*a^6-224*a^3+496*a^2+76- 276*a)*n-96-24*a^3+144*a+6*a^6+60*a^4-30*a^5-24*a^2)*v(n+3)+((30*a^2-28*a-20*a^3+16+ 5*a^4)*n^5+(45*a^4+270*a^2-252*a+144-180*a^3)*n^4+(750*a^2+400+125*a^4-700*a- 500*a^3)*n^3+(-420*a-300*a^3+450*a^2+240+75*a^4)*n^2+(-780*a^2+728*a+520*a^3-416- 130*a^4)*n-384-120*a^4+480*a^3+672*a-720*a^2)*v(n+4)+((-14*a^2+10*a^3+16*a+4+a^5- 5*a^4)*n^5+(15*a^5+240*a+150*a^3+60-210*a^2-75*a^4)*n^4+(340+850*a^3-1190*a^2+85*a^5+ 1360*a-425*a^4)*n^3+(3600*a+225*a^5+2250*a^3-3150*a^2-1125*a^4+900)*n^2+(274*a^5+ 2740*a^3+1096-3836*a^2-1370*a^4+4384*a)*n+480+1920*a+120*a^5-1680*a^2+1200*a^3- 600*a^4)*v(n+5): rec_p[29]:=(n-6)*v(n-5)+((-1+6*a)*n-29*a+5)*v(n-4)+((15*a^2-5*a-2)*n-55*a^2+8+19*a)*v(n-3)+ (n^3+(-6-8*a+20*a^3-10*a^2)*n+22*a-12-50*a^3+26*a^2)*v(n-2)+(5*n^3*a+6*n^2*a+(-10*a^3+ 15*a^4-12*a^2-14*a+2)*n+14*a^3-29*a+18*a^2-1-20*a^4)*v(n-1)+((-2+10*a^2)*n^3+(-4+ 24*a^2)*n^2+(-5*a^4-8*a^3+6*a^5+4*a+5*a^2+2)*n+2*a^3+a-16*a^2+a^4-a^5+5)*v(n)+((-1+ 10*a^3-6*a)*n^3+(-6-20*a+36*a^3)*n^2+(-18*a+39*a^3-12-2*a^4-a^5+2*a^2+a^6)*n+13*a^3+ 2*a^2-2*a^4-4*a-7+a^6-a^5)*v(n+1)+((-2*a+1+5*a^4-6*a^2)*n^3+(4-28*a^2+24*a^4-12*a)*n^2+ (-42*a^2+37*a^4-22*a+5)*n+2-12*a-20*a^2+18*a^4)*v(n+2)+((-a^2+a+1+a^5-2*a^3)*n^3+ (-12*a^3+6*a-6*a^2+6+6*a^5)*n^2+(-11*a^2+11*a^5+11+11*a-22*a^3)*n-12*a^3+6*a-6*a^2+ 6+6*a^5)*v(n+3): rec_p[30]:=(n-9)*v(n-8)+(-71*a+9*n*a)*v(n-7)+(n^3-22*n^2+(36*a^2+155)*n-350- 244*a^2)*v(n-6)+(9*n^3*a-170*n^2*a+(84*a^3+1023*a-1)*n-1966*a-476*a^3+3)*v(n-5)+ ((-4+36*a^2)*n^3+(-568*a^2+64)*n^2+(126*a^4-326+2832*a^2-6*a)*n-574*a^4-4484*a^2+ 530+14*a)*v(n-4)+((-28*a+84*a^3-1)*n^3+(10-1064*a^3+360*a)*n^2+(4200*a^3-36-1454*a+ 126*a^5-15*a^2)*n-5212*a^3-434*a^5+25*a^2+1854*a+25)*v(n-3)+((-6*a+126*a^4+6- 84*a^2)*n^3+(816*a^2-1204*a^4+44*a-60)*n^2+(84*a^6-20*a^3+182-118*a+3486*a^4- 2424*a^2)*n-3104*a^4+48*a-168-196*a^6+2220*a^2+20*a^3)*v(n-2)+((30*a-15*a^2-3- 140*a^3+126*a^5)*n^3+(-2-812*a^5+70*a^2+920*a^3-204*a)*n^2+(28-123*a^2+36*a^7-15*a^4+ 390*a-1720*a^3+1470*a^5)*n-208*a-760*a^5-44*a^7-49+916*a^3+5*a^4+8*a^2)*v(n-1)+ ((60*a^2-4+84*a^6-20*a^3-12*a-140*a^4)*n^3+(40*a^3+480*a^4-216*a^2-280*a^6-24*a+ 16)*n^2+(-6*a^5-11+144*a^2-310*a^4-32*a^3+38*a+168*a^6+9*a^8)*n-a^8+4*a^6-26*a- 20*a^3-1-6*a^4-2*a^5+4*a^2)*v(n)+((36*a^7-12*a-18*a^2-84*a^5+1-15*a^4+60*a^3)*n^3+ (-26-10*a^4+24*a^5-8*a^7-60*a^2+8*a-24*a^3)*n^2+(-88*a^3+21*a+114*a^5-48*a^7+a^9- 41*a^2-a^6+2*a^4-24)*n-a^6-3*a^4+6*a^5+a-4*a^3+a^2+3-4*a^7+a^9)*v(n+1)+((2*a-12*a^3- 6*a^5-12*a^2+30*a^4+9*a^8+1-28*a^6)*n^3+(-32*a^2-80*a^6+26*a^8-20*a^5+2-56*a^3-20*a+ 84*a^4)*n^2+(-12*a^2-74*a-1-44*a^6-18*a^5-84*a^3+15*a^8+42*a^4)*n-4*a^5-40*a^3-52*a- 2-12*a^4+8*a^2+8*a^6-2*a^8)*v(n+2)+((-a^6-3*a^4+6*a^5+a-4*a^3+a^2+3-4*a^7+a^9)*n^3+ (36*a^5-24*a^3+6*a+6*a^9+18+6*a^2-24*a^7-6*a^6-18*a^4)*n^2+(33+11*a^2+66*a^5-33*a^4- 44*a^3+11*a^9-11*a^6+11*a-44*a^7)*n+36*a^5-24*a^3+6*a+6*a^9+18+6*a^2-24*a^7-6*a^6- 18*a^4)*v(n+3): rec_p[31]:=v(n)+(2+3*n+n^2)*v(n+2): rec_p[32]:=(7*n+3-3*n^2)*v(n)+((-6*a-3)*n^2+(1-2*a)*n+4+4*a)*v(n+1)+((-3*a-3*a^2)*n^2+ (-9*a^2-9*a)*n-6*a^2-6*a)*v(n+2): rec_p[33]:=(2*n^3-4*n^2+2*n)*v(n-2)+((-5+10*a)*n^3+(2-4*a)*n^2+(-1+2*a)*n)*v(n-1)+((-20*a+ 4+20*a^2)*n^3+(6+24*a^2-24*a)*n^2+(-16*a+16*a^2+4)*n-4*a+2+4*a^2)*v(n)+((-1-30*a^2+12*a+ 20*a^3)*n^3+(36*a+56*a^3-84*a^2-4)*n^2+(-84*a^2+38*a+56*a^3-5)*n+14*a-2-30*a^2+ 20*a^3)*v(n+1)+((-2*a+12*a^2-20*a^3+10*a^4)*n^3+(-10*a+44*a^4-88*a^3+54*a^2)*n^2+ (62*a^4-16*a+78*a^2-124*a^3)*n+36*a^2+28*a^4-56*a^3-8*a)*v(n+2)+((-a^2+4*a^3-5*a^4+ 2*a^5)*n^3+(12*a^5-6*a^2+24*a^3-30*a^4)*n^2+(22*a^5+44*a^3-55*a^4-11*a^2)*n+12*a^5- 6*a^2+24*a^3-30*a^4)*v(n+3): rec_p[34]:=(2+3*n+n^2)*v(n)+((2*a+2)*n^2+(6*a+4)*n+4*a+2)*v(n+1)+((2*a+a^2)*n^2+(3*a^2+ 6*a)*n+2*a^2+4*a)*v(n+2): rec_p[35]:=(8-14*n*a+18*n^2*a+5*a)*v(n)+(6*a^3*n^2+12*a^3+18*a^3*n)*v(n+2)+(2*a^2+20*a^2*n+ 18*a^2*n^2)*v(n+1)+(-16*n+15+6*n^2)*v(n-1): rec_p[36]:=(2*n-n^2-1)*v(n-2)+((1-4*a)*n^2+(3*a-4)*n+5-a)*v(n-1)+((3*a-6*a^2)*n^2+(-3*a^2+ 2-5*a)*n-4+2*a-a^2)*v(n)+((3*a^2-4*a^3)*n^2+(2*a^2-7*a^3+2*a)*n-a^2+2*a-3*a^3)*v(n+1)+ ((-a^4+a^3)*n^2+(3*a^3-3*a^4)*n+2*a^3-2*a^4)*v(n+2):