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%I #16 Mar 08 2024 12:15:14
%S 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,
%T 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,
%U 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
%N 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).
%C 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).
%C 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.
%H Colin Barker, <a href="/A105966/b105966.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,-1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1).
%F a(n) = -a(n-5) + a(n-15) + a(n-20) for n>19. - _Colin Barker_, May 15 2019
%t 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 *)
%o (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
%K sign,easy
%O 0,21
%A _Creighton Dement_, Apr 28 2005
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