

A111913


Expansion of x*(23*xx^2+x^7+x^8+2*x^4) / ((x1)*(x+1)*(x^8x^4+1)).


4



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
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OFFSET

0,2


COMMENTS

It appears that (a(n)) has period 24.
The above conjecture is correct, since x^24 = 1 mod (x1)*(x+1)*(x^8x^4+1).  Charles R Greathouse IV, Feb 07 2013


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(n2) + a(n4)  a(n6)  a(n8) + a(n10) 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

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.
(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 * A210796 A305419 A075757
Adjacent sequences: A111910 A111911 A111912 * A111914 A111915 A111916


KEYWORD

easy,sign


AUTHOR

Creighton Dement, Aug 20 2005


STATUS

approved



