A087433 Expansion of g.f.: (1-2*x)*(1-4*x+x^2)/((1-x)*(1-3*x)*(1-4*x)).

1, 2, 6, 20, 70, 252, 926, 3460, 13110, 50252, 194446, 758100, 2973350, 11716252, 46333566, 183739940, 730176790, 2906358252, 11582386286, 46200404980, 184414199430, 736494536252, 2942491360606, 11759505089220, 47006639297270

Offset

0,2

Comments

Binomial transform of A087432. a(n+1) = 2*A085282(n).

Counts closed walks of length 2n at a vertex of the cyclic graph on 12 nodes C_12. - Herbert Kociemba, Jun 06 2004

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-19,12).

Formula

G.f.: (1-2*x)*(1-4*x+x^2)/((1-x)*(1-3*x)*(1-4*x)).

a(n) = 0^n/6 + 1/3 + 3^n/3 + 4^n/6.

a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3). - Wesley Ivan Hurt, Jul 11 2023

Mathematica

CoefficientList[Series[(1-2x)(1-4x+x^2)/((1-x)(1-3x)(1-4x)), {x, 0, 30}], x] (* Harvey P. Dale, Nov 26 2014 *)

Prog

(Magma) [0^n/6+1/3+3^n/3+4^n/6: n in [0..30]]; // Vincenzo Librandi, Aug 12 2011

Crossrefs

Cf. A085282, A087432.

Sequence in context: A071976 A302646 A000984 * A119373 A360292 A151284

Adjacent sequences: A087430 A087431 A087432 * A087434 A087435 A087436

Keyword

easy,nonn

Author

Paul Barry, Sep 02 2003

Extensions

Definition corrected by Herbert Kociemba, Jun 06 2004

Status

approved