A107849 Expansion of (1 + x)^2 / ((1 - x^2 - 2*x^3)*(1 + x^4)).

1, 2, 2, 4, 5, 6, 12, 16, 25, 42, 58, 92, 141, 206, 324, 488, 737, 1138, 1714, 2612, 3989, 6038, 9212, 14016, 21289, 32442, 49322, 75020, 114205, 173662, 264244, 402072, 611569, 930562, 1415714, 2153700, 3276837, 4985126, 7584236, 11538800

Offset: 0

Author

Creighton Dement, May 25 2005

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A107850, A107851, A107852.

Programs

Mathematica

CoefficientList[Series[(1 + x)^2 / ((1 - x^2 - 2*x^3)*(1 + x^4)),{x,0,39}],x] (* James C. McMahon, Feb 19 2024 *)

PARI

Vec((1 + x)^2 / ((1 - x^2 - 2*x^3)*(1 + x^4)) + O(x^45)) \\ Colin Barker, Apr 30 2019

Formula

a(n) = A052947(n+2) + A014017(n+6). - Ralf Stephan, Nov 30 2010

a(n) = a(n-2) + 2*a(n-3) - a(n-4) + a(n-6) + 2*a(n-7) for n>6. - Colin Barker, Apr 30 2019