OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (20,-160,640,-1280,1024).
FORMULA
a(n) = 4^n*(n^4 + 58*n^3 + 971*n^2 + 5114*n + 6144)/6144.
G.f.: (1 - 3*x)^4/(1 - 4*x)^5.
E.g.f.: (24 + 96*x + 72*x^2 + 16*x^3 + x^4)*exp(4*x)/24. - G. C. Greubel, Oct 18 2018
MATHEMATICA
LinearRecurrence[{20, -160, 640, -1280, 1024}, {1, 8, 54, 332, 1921}, 50] (* G. C. Greubel, Oct 18 2018 *)
PROG
(PARI) x='x+O('x^30); Vec((1-3*x)^4/(1-4*x)^5) \\ G. C. Greubel, Oct 18 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-3*x)^4/(1-4*x)^5)); // G. C. Greubel, Oct 18 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Mar 30 2003
STATUS
approved