A106835 Expansion of 2*x^2*(-2+9*x+3*x^2)/((2*x^2+5*x-1)*(2*x^2-5*x+1)).

0, 4, 22, 114, 590, 3066, 15998, 83786, 440270, 2320314, 12260382, 64931114, 344562670, 1831630106, 9751275838, 51981730186, 277413656590, 1481919831674, 7922862005342, 42388551182314, 226923616315950, 1215450062928346

Offset

1,2

Links

Table of n, a(n) for n=1..22.

Index entries for linear recurrences with constant coefficients, signature (10,-25,0,4).

Formula

From R. J. Mathar, Apr 07 2009: (Start)

G.f.: 2*x^2*(-2+9*x+3*x^2)/((2*x^2+5*x-1)*(2*x^2-5*x+1)).

a(n) = (-7*A107839(n)+33*A107839(n-1)+A015535(n+1)-3*A015535(n))/4.

a(n) = 10*a(n-1)-25*a(n-2)+4*a(n-4). (End)

Mathematica

M = {{0, 0, 0, 2}, {1, 5, 0, 0}, {0, 2, 0, 0}, {0, 0, 1, 5}};
v[1] = {0, 1, 1, 2};
v[n_] := v[n] = M.v[n - 1];
a = Table[v[n][[1]], {n, 1, 50}]
LinearRecurrence[{10, -25, 0, 4}, {0, 4, 22, 114}, 30] (* Harvey P. Dale, Jul 05 2025 *)

Crossrefs

Sequence in context: A274799 A290591 A272435 * A293966 A305554 A291183

Adjacent sequences: A106832 A106833 A106834 * A106836 A106837 A106838

Keyword

nonn,easy,less

Author

Roger L. Bagula, May 30 2005

Extensions

Edited by Associate Editors of the OEIS, Apr 05 2009

Meaningful name from Joerg Arndt, Dec 26 2022

Status

approved