OFFSET
0,2
COMMENTS
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, -15).
FORMULA
G.f.: (t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(15*t^33 - 5*t^32 - 5*t^31 - 5*t^30 - 5*t^29 - 5*t^28 - 5*t^27 - 5*t^26 - 5*t^25 - 5*t^24 - 5*t^23 - 5*t^22 - 5*t^21 - 5*t^20 - 5*t^19 - 5*t^18 - 5*t^17 - 5*t^16 - 5*t^15 - 5*t^14 - 5*t^13 - 5*t^12 - 5*t^11 - 5*t^10 - 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1).
G.f.: (1+x)*(1-x^33)/(1 - 6*x + 20*x^33 - 15*x^34). - G. C. Greubel, May 01 2019
a(n) = -15*a(n-33) + 5*Sum_{k=1..32} a(n-k). - Wesley Ivan Hurt, May 06 2021
MAPLE
gf:= (t+1) *(t^2+t+1) *(t^10+t^9+t^8+t^7+t^6+t^5+t^4+t^3+t^2+t+1) *(t^20-t^19+t^17-t^16 +t^14-t^13+t^11-t^10+t^9-t^7+t^6-t^4+t^3- t+1) / (15*t^33-5*t^32-5*t^31-5*t^30-5*t^29 -5*t^28-5*t^27 -5*t^26-5*t^25 -5*t^24 -5*t^23-5*t^22-5*t^21-5*t^20 -5*t^19-5*t^18-5*t^17 -5*t^16 -5*t^15 -5*t^14-5*t^13-5*t^12-5*t^11-5*t^10-5*t^9-5*t^8-5*t^7 -5*t^6 -5*t^5-5*t^4 -5*t^3-5*t^2-5*t+1):
S:= series(gf, t, 101):
seq(coeff(S, t, j), j=0..100); # Robert Israel, Aug 26 2014
MATHEMATICA
coxG[{pwr_, c1_, c2_, trms_:20}]:=Module[{num=Total[2t^Range[pwr-1]]+t^pwr+ 1, den =Total[c2*t^Range[pwr-1]]+c1*t^pwr+1}, CoefficientList[ Series[ num/den, {t, 0, trms}], t]]; coxG[{33, 15, -5, 30}]
(* "pwr" is the largest exponent in the g.f.;
"c1" is the first coefficient in the denominator of the g.f.;
"c2" is the second coefficient in the denominator of the g.f.;
"trms" is the number of terms desired (with a default number of 20) *)
(* Harvey P. Dale, Aug 16 2014 *)
CoefficientList[Series[(1+x)*(1-x^33)/(1-6*x+20*x^33-15*x^34), {x, 0, 25}], x] (* G. C. Greubel, May 01 2019 *)
PROG
(PARI) my(x='x+O('x^25)); Vec((1+x)*(1-x^33)/(1-6*x+20*x^33-15*x^34)) \\ G. C. Greubel, May 01 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 25); Coefficients(R!( (1+x)*(1-x^3)/(1-14*x+104*x^3-91*x^4) )); // G. C. Greubel, May 01 2019
(Sage) ((1+x)*(1-x^33)/(1-6*x+20*x^33-15*x^34)).series(x, 25).coefficients(x, sparse=False) # G. C. Greubel, May 01 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved