A077852 Expansion of (1-x)^(-1)/(1-2*x-x^3).

1, 3, 7, 16, 36, 80, 177, 391, 863, 1904, 4200, 9264, 20433, 45067, 99399, 219232, 483532, 1066464, 2352161, 5187855, 11442175, 25236512, 55660880, 122763936, 270764385, 597189651, 1317143239, 2905050864, 6407291380, 14131726000, 31168502865, 68744297111

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2,1,-1).

Crossrefs

Cf. A019489. - R. J. Mathar, Sep 19 2008

Programs

Maple

a:= n-> (<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <-1|1|-2|3>>^n)[4,4]:
seq(a(n), n=0..30);  # Alois P. Heinz, Nov 12 2017

Mathematica

CoefficientList[Series[(1-x)^(-1)/(1-2x-x^3),{x,0,40}],x] (* or *) LinearRecurrence[{3,-2,1,-1},{1,3,7,16},40] (* Harvey P. Dale, Oct 05 2012 *)

Formula

From R. J. Mathar, May 15 2008: (Start)

a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) - a(n-4).

a(n+1) - a(n) = A008998(n+1). (End)

a(n) = 2*a(n-1) + a(n-3) + 1. - Greg Dresden, Apr 04 2021