A122508 G.f.: 1/[(1-2x)(1+2x+3x^2)].

1, 0, 1, 6, 1, 12, 37, 18, 109, 240, 217, 894, 1657, 2196, 7021, 12138, 20197, 54264, 93025, 175446, 418609, 733596, 1471285, 3245250, 5872861, 12072960, 25344361, 47310126, 97782121, 199376292, 381642877, 786069018, 1577900629, 3075926280

Offset

0,4

Comments

G.f.=1/[x^3*p(1/x)], where p(x)=x^3-x-6

(1,6)-Padovan sequence with o.g.f. 1/(1-x^2-6*x^3). See A000931(n+3)for (1,1)Padovan, and the W. Lang link given there for an explicit formula and a combinatorial interpretation. [From Wolfdieter Lang, Jun 28 2010]

Links

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (0,1,6).

Formula

a(n+1) = (7*b(n) + 6*b(n-1) + 2^(n+2))/11, with b(n):=A088137(n+1)*(-1)^n. From the o.g.f. ((7+6*x)/(1+2*x+3*x^2)+ 4/(1-2*x))/11. [From Wolfdieter Lang, Jun 28 2010]

Maple

G:=x/(1-2*x)/(1+2*x+3*x^2): Gser:=series(G, x=0, 41): seq(coeff(Gser, x, n), n=0..38);

Mathematica

p[x_]=-6 - x + x^3 q[x_] = ExpandAll[x^3*p[1/x]] Table[ SeriesCoefficient[Series[x/q[x], {x, 0, 30}], n], {n, 0, 30}]

Crossrefs

Sequence in context: A090850 A163945 A013613 * A171006 A176121 A062190

Adjacent sequences: A122505 A122506 A122507 * A122509 A122510 A122511

Keyword

nonn,easy

Author

Roger L. Bagula, Sep 15 2006

Extensions

Edited by N. J. A. Sloane, Oct 08 2006

Status

approved