A091919 Expansion of 1/((1-2*x)*(1-x^2)^2).

1, 2, 6, 12, 27, 54, 112, 224, 453, 906, 1818, 3636, 7279, 14558, 29124, 58248, 116505, 233010, 466030, 932060, 1864131, 3728262, 7456536, 14913072, 29826157, 59652314, 119304642, 238609284, 477218583, 954437166, 1908874348, 3817748696

Offset: 0

Author

Paul Barry, Feb 13 2004

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,2,-4,-1,2).

Programs

Magma

[2^(n+4)/9 + (3*n+8)*(-1)^n/36 - (n+4)/4: n in [0..30]]; // G. C. Greubel, Oct 11 2017

Mathematica

CoefficientList[Series[1/((1 - 2*x)*(1 - x^2)^2), {x, 0, 50}], x] (* G. C. Greubel, Oct 11 2017 *)
LinearRecurrence[{2,2,-4,-1,2},{1,2,6,12,27},40] (* Harvey P. Dale, Oct 23 2019 *)

PARI

for(n=0, 50, print1(2^(n+4)/9 + (3*n+8)*(-1)^n/36 - (n+4)/4, ", ")) \\ G. C. Greubel, Oct 11 2017

Formula

a(n) = 2^(n+4)/9 + (3*n+8)*(-1)^n/36 - (n+4)/4.

a(n) = Sum_{k=0..floor(n/2)} A000975(n-2*k+1). - Paul Barry, Jan 18 2009