A077863 Expansion of (1-x)^(-1)/(1-x-2*x^2-2*x^3).

1, 2, 5, 12, 27, 62, 141, 320, 727, 1650, 3745, 8500, 19291, 43782, 99365, 225512, 511807, 1161562, 2636201, 5982940, 13578467, 30816750, 69939565, 158730000, 360242631, 817581762, 1855527025, 4211175812, 9557393387, 21690799062, 49227937461, 111724322360

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (2,1,0,-2).

Crossrefs

Cf. A077946 (first differences).

Cf. A078006 (second differences).

Programs

Mathematica

CoefficientList[Series[(1-x)^(-1)/(1-x-2x^2-2x^3),{x,0,40}],x] (* or *) LinearRecurrence[{2,1,0,-2},{1,2,5,12},40] (* Harvey P. Dale, Sep 14 2016 *)

PARI

my(x='x+O('x^40)); Vec((1-x)^(-1)/(1-x-2*x^2-2*x^3)) \\ Christian Krause, Jan 02 2023

Formula

a(n) = a(n-1) + 2*a(n-2) + 2*a(n-3) + 1. - Christian Krause, Jan 02 2023