A097120 Expansion of (1-x)^2/((1-x)^3-3x^4).

1, 1, 1, 1, 4, 13, 31, 61, 115, 232, 505, 1117, 2413, 5089, 10660, 22477, 47779, 101833, 216619, 459568, 974017, 2065465, 4383769, 9307633, 19759108, 41934589, 88985383, 188834389, 400758931, 850562776, 1805202073, 3831179989

Offset

0,5

Links

Table of n, a(n) for n=0..31.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1,3).

Formula

G.f. : (1-2x+x^2)/(1-3x+3x^2-x^3-3x^4); a(n)=3a(n-1)-3a(n-2)+a(n-3)+3a(n-4); a(n)=sum{k=0..floor(n/3), binomial(n-k, 3k)3^k}.

Mathematica

CoefficientList[Series[(1-x)^2/((1-x)^3-3x^4), {x, 0, 40}], x] (* or *) LinearRecurrence[{3, -3, 1, 3}, {1, 1, 1, 1}, 40] (* Harvey P. Dale, Aug 25 2023 *)

Crossrefs

Sequence in context: A106302 A158842 A100136 * A098536 A216563 A011937

Adjacent sequences: A097117 A097118 A097119 * A097121 A097122 A097123

Keyword

easy,nonn

Author

Paul Barry, Jul 25 2004

Status

approved