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 (24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,-300).
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)/( 300*t^16 - 24*t^15 - 24*t^14 - 24*t^13 - 24*t^12 - 24*t^11 - 24*t^10 - 24*t^9 - 24*t^8 - 24*t^7 - 24*t^6 - 24*t^5 - 24*t^4 - 24*t^3 - 24*t^2 - 24*t + 1).
From G. C. Greubel, Sep 08 2023: (Start)
G.f.: (1+t)*(1-t^16)/(1 - 25*t + 324*t^16 - 300*t^17).
a(n) = 24*Sum_{j=1..15} a(n-j) - 300*a(n-16). (End)
MATHEMATICA
coxG[{16, 300, -24}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 01 2021 *)
CoefficientList[Series[(1+t)*(1-t^16)/(1-25*t+324*t^16-300*t^17), {t, 0, 50}], t] (* G. C. Greubel, Sep 08 2023 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-25*x+324*x^16-300*x^17) )); // G. C. Greubel, Sep 08 2023
(SageMath)
def A167941_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x)*(1-x^16)/(1-25*x+324*x^16-300*x^17) ).list()
A167941_list(40) # G. C. Greubel, Sep 08 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved