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 (4,4,4,4,4,4,4,4,4,4,4,-10).
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)/(10*t^12 - 4*t^11 - 4*t^10 - 4*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t + 1).
From G. C. Greubel, Aug 03 2024: (Start)
a(n) = 4*Sum_{j=1..11} a(n-j) - 10*a(n-12).
G.f.: (1+x)*(1-x^12)/(1 - 5*x + 14*x^12 - 10*x^13). (End)
MATHEMATICA
With[{p=10, q=4}, CoefficientList[Series[(1+t)*(1-t^12)/(1 - (q+1)*t + (p+q)*t^12 - p*t^13), {t, 0, 40}], t]] (* G. C. Greubel, May 15 2016; Aug 02 2024 *)
coxG[{12, 10, -4, 30}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 03 2024 *)
PROG
(Magma)
R<x>:=PowerSeriesRing(Integers(), 30);
f:= func< p, q, x | (1+x)*(1-x^12)/(1-(q+1)*x+(p+q)*x^12-p*x^13) >;
Coefficients(R!( f(10, 4, x) )); // G. C. Greubel, Aug 03 2024
(SageMath)
def f(p, q, x): return (1+x)*(1-x^12)/(1-(q+1)*x+(p+q)*x^12-p*x^13)
def A166500_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( f(10, 4, x) ).list()
A166500_list(30) # G. C. Greubel, Aug 03 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved