A105964 Expansion of x*(1+x^3-x^6+x^7)/(1-x^6)^2.

0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 2, 0, 0, 1, 2, 0, 3, 0, 0, 1, 3, 0, 4, 0, 0, 1, 4, 0, 5, 0, 0, 1, 5, 0, 6, 0, 0, 1, 6, 0, 7, 0, 0, 1, 7, 0, 8, 0, 0, 1, 8, 0, 9, 0, 0, 1, 9, 0, 10, 0, 0, 1, 10, 0, 11, 0, 0, 1, 11, 0, 12, 0, 0, 1, 12, 0, 13, 0, 0, 1, 13, 0, 14, 0, 0, 1, 14, 0, 15, 0, 0, 1, 15, 0, 16, 0, 0, 1

Offset

0,11

Comments

Floretion Algebra Multiplication Program, FAMP Code: 2jbasekfizrokseq[.5'i + .5'ii' - .5'ij' + .5'ik'], RokType: Y[sqa.Findk()] = Y[sqa.Findk()] + 1 (internal program code). FizType: 'i, 'j, 'k.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,2,0,0,0,0,0,-1).

Formula

G.f.: x*(1+x^3-x^6+x^7)/((1-x)*(1+x)*(1+x+x^2)*(1-x+x^2))^2.

a(n) = 2*a(n-6) - a(n-12) for n>11. - Colin Barker, May 13 2019

Maple

seq(coeff(series(x*(1+x^3-x^6+x^7)/(1-x^6)^2, x, n+1), x, n), n = 0..100); # G. C. Greubel, Jan 15 2020

Mathematica

CoefficientList[Series[x(1+x^3-x^6+x^7)/(1-x^6)^2, {x, 0, 100}], x] (* or *) LinearRecurrence[{0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1}, {0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 2, 0}, 100] (* Harvey P. Dale, Aug 08 2019 *)

Prog

(PARI) concat(0, Vec(x*(1 +x^3 -x^6 +x^7)/(1-x^6)^2 + O(x^100))) \\ Colin Barker, May 13 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 100); Coefficients(R!( x*(1+x^3-x^6+x^7)/(1-x^6)^2 )); // G. C. Greubel, Jan 15 2020
(SageMath)
def A105964_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( x*(1+x^3-x^6+x^7)/(1-x^6)^2 ).list()
A105964_list(100) # G. C. Greubel, Jan 15 2020
(GAP) a:=[0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 2, 0];; for n in [13..100] do a[n]:=2*a[n-6]-a[n-12]; od; a; # G. C. Greubel, Jan 15 2020

Crossrefs

Sequence in context: A035217 A357237 A277808 * A303051 A324044 A364046

Adjacent sequences: A105961 A105962 A105963 * A105965 A105966 A105967

Keyword

nonn,easy

Author

Creighton Dement, Apr 28 2005

Status

approved