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 (16,-96,256,-256)
FORMULA
a(n) = 4^n*(n^3 + 33*n^2 + 254*n + 384)/384.
G.f.: (1 - 3*x)^3/(1 - 4*x)^4.
E.g.f.: (6 + 18*x + 9*x^2 + x^3)*exp(4*x)/6. - G. C. Greubel, Oct 18 2018
MATHEMATICA
LinearRecurrence[{16, -96, 256, -256}, {1, 7, 43, 245}, 50] (* G. C. Greubel, Oct 18 2018 *)
CoefficientList[Series[(1-3x)^3/(1-4x)^4, {x, 0, 30}], x] (* Harvey P. Dale, Nov 30 2021 *)
PROG
(PARI) x='x+O('x^30); Vec((1-3*x)^3/(1-4*x)^4) \\ G. C. Greubel, Oct 18 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-3*x)^3/(1-4*x)^4)); // G. C. Greubel, Oct 18 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Mar 30 2003
STATUS
approved