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A106666 Expansion of g.f. (1-4*x^2+2*x^3)/((1-x)*(1-2*x-2*x^2+2*x^3)). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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).

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.

MATHEMATICA

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

PROG

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

(Magma) R<x>:=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

(Sage)

def A106666_list(prec):

    P.<x> = 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

CROSSREFS

Cf. A052970, A052987, A077937.

Sequence in context: A339155 A168314 A335562 * A124791 A147046 A233232

Adjacent sequences:  A106663 A106664 A106665 * A106667 A106668 A106669

KEYWORD

easy,nonn

AUTHOR

Creighton Dement, May 13 2005

STATUS

approved

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Last modified September 30 20:49 EDT 2022. Contains 357106 sequences. (Running on oeis4.)