A106666 Expansion of g.f. (1-4*x^2+2*x^3)/((1-x)*(1-2*x-2*x^2+2*x^3)).

1, 3, 5, 13, 29, 73, 177, 441, 1089, 2705, 6705, 16641, 41281, 102433, 254145, 630593, 1564609, 3882113, 9632257, 23899521, 59299329, 147133185, 365065985, 905799681, 2247464961, 5576397313, 13836125185, 34330115073, 85179685889

Offset: 0

Author

Creighton Dement, May 13 2005

Keywords

• easy
• nonn

Comments

Floretion Algebra Multiplication Program, FAMP Code: 1vesseq[I*J*cyc(I)] with I = + .5'ii' + .5'kk' + .5'ik' + .5'jk' + .5'ki' + .5'kj' and J = + .5'i + .5i' - .5'ii' + .5'jj' + .5'kk' + .5e

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,0,-4,2).

Crossrefs

Cf. A052970, A052987, A077937.

Programs

Magma

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!(  (1-4*x^2+2*x^3)/((1-x)*(1-2*x-2*x^2+2*x^3)) )); // G. C. Greubel, Sep 08 2021

Mathematica

LinearRecurrence[{3,0,-4,2},{1,3,5,13},30] (* Harvey P. Dale, Jul 28 2015 *)

SageMath

def A106666_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( (1-4*x^2+2*x^3)/((1-x)*(1-2*x-2*x^2+2*x^3)) ).list()
A106666_list(50) # G. C. Greubel, Sep 08 2021

Formula

Superseeker results: a(n+1) - a(n) = A052970(n+2); a(n+2) - a(n) = A052987(n+2).

a(0)=1, a(n) = 2*A077937(n-1) + 1.