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A111913 Expansion of x*(-2-3*x-x^2+x^7+x^8+2*x^4) / ((x-1)*(x+1)*(x^8-x^4+1)). 4

%I

%S 0,2,3,3,3,3,6,4,5,1,5,1,4,-2,1,-3,1,-3,-2,-4,-1,-1,-1,-1,0,2,3,3,3,3,

%T 6,4,5,1,5,1,4,-2,1,-3,1,-3,-2,-4,-1,-1,-1,-1,0,2,3,3,3,3,6,4,5,1,5,1,

%U 4,-2,1,-3,1,-3,-2,-4,-1,-1,-1,-1,0,2,3,3,3,3,6,4,5,1,5,1,4,-2,1,-3,1,-3,-2,-4,-1,-1,-1,-1,0,2,3,3

%N Expansion of x*(-2-3*x-x^2+x^7+x^8+2*x^4) / ((x-1)*(x+1)*(x^8-x^4+1)).

%C It appears that (a(n)) has period 24.

%C The above conjecture is correct, since x^24 = 1 mod (x-1)*(x+1)*(x^8-x^4+1). - _Charles R Greathouse IV_, Feb 07 2013

%H Colin Barker, <a href="/A111913/b111913.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,1,0,-1,0,-1,0,1).

%F a(n) = a(n-2) + a(n-4) - a(n-6) - a(n-8) + a(n-10) for n>9. - _Colin Barker_, May 18 2019

%t LinearRecurrence[{0,1,0,1,0,-1,0,-1,0,1},{0,2,3,3,3,3,6,4,5,1},120] (* _Harvey P. Dale_, Apr 14 2019 *)

%o Floretion Algebra Multiplication Program, FAMP Code: 4ibasesigcycsumseq[ + .5'i + .5j' + .5'ij' + .5e], sumtype: Y[8] = (int)Y[6] - (int)Y[7] + Y[8] + sum (internal program code); apart from initial term 0.

%o (PARI) a(n)=[0,2,3,3,3,3,6,4,5,1,5,1,4,-2,1,-3,1,-3,-2,-4,-1,-1,-1,-1][n%24+1] \\ _Charles R Greathouse IV_, Feb 07 2013

%o (PARI) concat(0, Vec(x*(2 + 3*x + x^2 - 2*x^4 - x^7 - x^8) / ((1 - x)*(1 + x)*(1 - x^4 + x^8)) + O(x^80))) \\ _Colin Barker_, May 18 2019

%Y Cf. A111912, A111914, A111915, A085846.

%K easy,sign

%O 0,2

%A _Creighton Dement_, Aug 20 2005

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Last modified July 26 13:40 EDT 2021. Contains 346294 sequences. (Running on oeis4.)