OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,-6).
FORMULA
G.f.: (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)/ ( 6*t^16 - 3*t^15 - 3*t^14 - 3*t^13 - 3*t^12 - 3*t^11 - 3*t^10 - 3*t^9 - 3*t^8 - 3*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1).
From G. C. Greubel, Dec 06 2024: (Start)
a(n) = 3*Sum_{j=1..15} a(n-j) - 6*a(n-16).
G.f.: (1+x)*(1-x^16)/(1 - 4*x + 9*x^16 - 6*x^17). (End)
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^16)/(1-4*t+9*t^16-6*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 01 2016; Dec 06 2024 *)
coxG[{16, 6, -3, 40}] (* The coxG program is at A169452 *) (* G. C. Greubel, Dec 06 2024 *)
PROG
(Magma)
R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-4*x+9*x^16-6*x^17) )); // G. C. Greubel, Dec 06 2024
(SageMath)
def A167896_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x)*(1-x^16)/(1-4*x+9*x^16-6*x^17) ).list()
print(A167896_list(40)) # G. C. Greubel, Dec 06 2024
(PARI) Vec((x^16+2*x^15+2*x^14+2*x^13+2*x^12+2*x^11+2*x^10+2*x^9+2*x^8+2*x^7+2*x^6+2*x^5+2*x^4+2*x^3+2*x^2+2*x+1)/(6*x^16-3*x^15-3*x^14-3*x^13-3*x^12-3*x^11-3*x^10-3*x^9-3*x^8-3*x^7-3*x^6-3*x^5-3*x^4-3*x^3-3*x^2-3*x+1)+O(x^99)) \\ Charles R Greathouse IV, May 15 2026
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved
