A120463 Expansion of x*(1+x+2*x^3) / ((x-1)*(1+x)*(3*x^2-1)).

0, 1, 1, 4, 6, 13, 21, 40, 66, 121, 201, 364, 606, 1093, 1821, 3280, 5466, 9841, 16401, 29524, 49206, 88573, 147621, 265720, 442866, 797161, 1328601, 2391484, 3985806, 7174453, 11957421, 21523360, 35872266, 64570081, 107616801, 193710244

Offset

0,4

Comments

Top element of the vector obtained by multiplying the n-th power of the 5 X 5 matrix [[0, 1, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0]] by the column vector [0, 1, 1, 2, 3].

Links

Table of n, a(n) for n=0..35.

Index entries for linear recurrences with constant coefficients, signature (0,4,0,-3).

Formula

G.f.: x*(1+x+2*x^3) / ((x-1)*(1+x)*(3*x^2-1)).

a(2n+2) = A134931(n). a(2n+1) = A003462(n+1). - R. J. Mathar, Nov 07 2011

Mathematica

LinearRecurrence[{0, 4, 0, -3}, {0, 1, 1, 4, 6}, 40] (* Harvey P. Dale, Dec 15 2018 *)

Crossrefs

Cf. A003462, A134931.

Sequence in context: A013122 A012964 A284798 * A049732 A262194 A136391

Adjacent sequences: A120460 A120461 A120462 * A120464 A120465 A120466

Keyword

nonn,easy

Author

Roger L. Bagula and Gary W. Adamson, Jun 30 2006

Status

approved