A106851 Expansion of (-3*x^3 - 7*x^2 + 2*x)/((1-4*x-x^2)*(1-4*x+x^2)).

0, 2, 9, 37, 152, 626, 2585, 10701, 44400, 184610, 769065, 3209461, 13415048, 56153618, 235357241, 987609501, 4148575200, 17443003202, 73402179657, 309116995525, 1302649664888, 5492768393906, 23173154692697, 97810060234605

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Index entries for linear recurrences with constant coefficients, signature (8, -16, 0, 1).

Formula

G.f.: (-3*x^3 - 7*x^2 + 2*x)/((1-4*x-x^2)*(1-4*x+x^2)).

a(n) = (1/2) * [A001834(n-1) + Fibonacci(3n+1) ]. - Ralf Stephan, Nov 18 2010

a(0)=0, a(1)=2, a(2)=9, a(3)=37, a(n)=8*a(n-1)-16*a(n-2)+a(n-4) [Harvey P. Dale, Aug 05 2011]

Mathematica

CoefficientList[Series[(-3 x^3-7x^2+2x)/((1-4x-x^2)(1-4x+x^2)), {x, 0, 30}], x] (* or *) LinearRecurrence[{8, -16, 0, 1}, {0, 2, 9, 37}, 31] (* Harvey P. Dale, Aug 05 2011 *)

Crossrefs

Sequence in context: A037553 A178875 A012493 * A129169 A162548 A150983

Adjacent sequences: A106848 A106849 A106850 * A106852 A106853 A106854

Keyword

nonn,easy

Author

Roger L. Bagula, May 30 2005

Extensions

Edited by N. J. A. Sloane, Apr 09 2007

New name from Joerg Arndt, Dec 26 2022

Status

approved