A105966 Expansion of A/B with A = (-1+x^15-x^10-x^9-x^8-2*x^5-x^4) and B = (x-1)*(x+1)*(x^2+x+1)*(x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1)*(x^8-x^7+x^5-x^4+x^3-x+1).

1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0

Offset

0,21

Comments

Sequence appears to be periodic with initial period (1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0). (Period 30).

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

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,-1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1).

Formula

a(n) = -a(n-5) + a(n-15) + a(n-20) for n>19. - Colin Barker, May 15 2019

Mathematica

LinearRecurrence[{0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 1}, 120] (* Harvey P. Dale, Sep 05 2022 *)

Prog

(PARI) Vec((1 + x^4 + 2*x^5 + x^8 + x^9 + x^10 - x^15) / ((1 - x)*(1 + x)*(1 + x + x^2)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)*(1 - x + x^3 - x^4 + x^5 - x^7 + x^8)) + O(x^100)) \\ Colin Barker, May 15 2019

Crossrefs

Sequence in context: A216511 A138088 A112765 * A318950 A319000 A083915

Adjacent sequences: A105963 A105964 A105965 * A105967 A105968 A105969

Keyword

sign,easy

Author

Creighton Dement, Apr 28 2005

Status

approved