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 (23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,-276).
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)/( 276*t^16 - 23*t^15 - 23*t^14 - 23*t^13 - 23*t^12 - 23*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).
From G. C. Greubel, Sep 08 2023: (Start)
G.f.: (1+t)*(1-t^16)/(1 - 24*t + 299*t^16 - 276*t^17).
a(n) = 23*Sum_{j=1..15} a(n-j) - 276*a(n-16). (End)
MATHEMATICA
coxG[{16, 276, -23}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 05 2015 *)
CoefficientList[Series[(1+t)*(1-t^16)/(1-24*t+299*t^16-276*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 01 2016; Sep 08 2023 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-24*x+299*x^16-276*x^17) )); // G. C. Greubel, Sep 08 2023
(SageMath)
def A167940_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x)*(1-x^16)/(1-24*x+299*x^16-276*x^17) ).list()
A167940_list(40) # G. C. Greubel, Sep 08 2023
(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)/(276*x^16-23*x^15-23*x^14-23*x^13-23*x^12-23*x^11-23*x^10-23*x^9-23*x^8-23*x^7-23*x^6-23*x^5-23*x^4-23*x^3-23*x^2-23*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
