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 (45,45,45,45,45,45,45,45,45,45,-1035).
FORMULA
G.f.: (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)/(1035*t^11 - 45*t^10 - 45*t^9 - 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1).
From G. C. Greubel, Jul 26 2024: (Start)
a(n) = 45*Sum_{j=1..10} a(n-j) - 1035*a(n-11).
G.f.: (1+x)*(1-x^11)/(1 - 46*x + 1080*x^11 - 1035*x^12). (End)
MATHEMATICA
coxG[{11, 1035, -45}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 16 2015 *)
With[{p=1035, q=45}, CoefficientList[Series[(1+t)*(1-t^11)/(1 - (q+1)*t + (p+q)*t^11 - p*t^12), {t, 0, 40}], t]] (* G. C. Greubel, May 14 2016; Jul 26 2024 *)
PROG
(Magma)
R<x>:=PowerSeriesRing(Integers(), 30);
f:= func< p, q, x | (1+x)*(1-x^11)/(1-(q+1)*x+(p+q)*x^11-p*x^12) >;
Coefficients(R!( f(1035, 45, x) )); // G. C. Greubel, Jul 26 2024
(SageMath)
def f(p, q, x): return (1+x)*(1-x^11)/(1-(q+1)*x+(p+q)*x^11-p*x^12)
def A166441_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( f(1035, 45, x) ).list()
A166441_list(30) # G. C. Greubel, Jul 26 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved