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)).

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, 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, 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

Offset

0,2

Comments

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

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

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.

Links

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

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

Formula

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

Mathematica

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 *)

Prog

(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
(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

Crossrefs

Cf. A111912, A111914, A111915, A085846.

Sequence in context: A147815 A227246 A200924 * A354142 A210796 A305419

Adjacent sequences: A111910 A111911 A111912 * A111914 A111915 A111916

Keyword

easy,sign

Author

Creighton Dement, Aug 20 2005

Status

approved