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 (10,10,10,10,10,10,10,10,10,10,10,-55).
FORMULA
G.f.: (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)/(55*t^12 - 10*t^11 - 10*t^10 - 10*t^9 - 10*t^8 - 10*t^7 - 10*t^6 - 10*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t +1).
From G. C. Greubel, Dec 03 2024: (Start)
a(n) = 10*Sum_{j=1..11} a(n-j) - 55*a(n-12).
G.f.: (1+t)*(1 - t^12)/(1 - 11*t + 65*t^12 - 55*t^13). (End)
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^12)/(1-11*t+65*t^12-55*t^13), {t, 0, 50}], t]
(* G. C. Greubel, May 17 2016; Dec 03 2024 *)
coxG[{12, 55, -10}] (* The coxG program is at A169452 *) (* G. C. Greubel, Dec 03 2024 *)
PROG
(Magma)
R<x>:=PowerSeriesRing(Integers(), 40);
Coefficients(R!( (1+x)*(1-x^12)/(1-11*x+65*x^12-55*x^13) )); // ~~~
(SageMath)
def A166557_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x)*(1-x^12)/(1-11*x+65*x^12-55*x^13) ).list()
A166557_list(40) # G. C. Greubel, Dec 03 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved