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 (6,6,6,6,6,6,6,6,6,6,6,-21).
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)/(21*t^12 - 6*t^11 - 6*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1).
From G. C. Greubel, Aug 23 2024: (Start)
a(n) = 6*Sum_{j=1..11} a(n-j) - 21*a(n-12).
G.f.: (1 + x)*(1 - x^12)/(1 - 7*x + 27*x^12 - 21*x^13). (End)
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^12)/(1-7*t+27*t^12-21*t^13), {t, 0, 50}], t] (* G. C. Greubel, May 16 2016; Aug 23 2024 *)
coxG[{12, 21, -6}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 24 2016 *)
PROG
(Magma)
R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^12)/(1-7*x+27*x^12-21*x^13) )); // G. C. Greubel, Aug 23 2024
(SageMath)
def A166538_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x)*(1-x^12)/(1-7*x+27*x^12-21*x^13) ).list()
A166538_list(30) # G. C. Greubel, Aug 23 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved