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 (22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,-253).
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)/( 253*t^16 - 22*t^15 - 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).
From G. C. Greubel, Sep 09 2023: (Start)
G.f.: (1+t)*(1-t^16)/(1 - 23*t + 275*t^16 - 253*t^17).
a(n) = 22*Sum_{j=1..15} a(n-j) - 253*a(n-16). (End)
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^16)/(1-23*t+275*t^16-253*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 01 2016; Sep 09 2023 *)
coxG[{16, 253, -22}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 18 2022 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-23*x+275*x^16-253*x^17) )); // G. C. Greubel, Sep 09 2023
(SageMath)
def A167938_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x)*(1-x^16)/(1-23*x+275*x^16-253*x^17) ).list()
A167938_list(40) # G. C. Greubel, Sep 09 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)/(253*x^16-22*x^15-22*x^14-22*x^13-22*x^12-22*x^11-22*x^10-22*x^9-22*x^8-22*x^7-22*x^6-22*x^5-22*x^4-22*x^3-22*x^2-22*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
