A109785 Expansion of (1+x+x^2+x^7+x^8-2*x^10-x^12) / ((x+1)*(x^2+1)*(x^2+x+1)*(x^2-x+1)*(x^4-x^2+1)*(x-1)^2).

1, 2, 3, 3, 3, 3, 3, 4, 5, 5, 3, 3, 3, 4, 5, 5, 5, 5, 5, 6, 7, 7, 5, 5, 5, 6, 7, 7, 7, 7, 7, 8, 9, 9, 7, 7, 7, 8, 9, 9, 9, 9, 9, 10, 11, 11, 9, 9, 9, 10, 11, 11, 11, 11, 11, 12, 13, 13, 11, 11, 11, 12, 13, 13, 13, 13, 13, 14, 15, 15, 13, 13, 13, 14, 15, 15, 15, 15, 15, 16, 17, 17, 15, 15, 15

Offset

0,2

Comments

Floretion Algebra Multiplication Program, FAMP Code: 1jbasesumseq[(- .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki')*(- .5'i + .5'j - .5i' + .5j' - 'kk' - .5'ik' - .5'jk' - .5'ki' - .5'kj')], sumtype: (default, ver. f, ves)

Links

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

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

Formula

a(n) = a(n-1) + a(n-12) - a(n-13) for n>12. - Colin Barker, May 15 2019

Mathematica

CoefficientList[Series[(1+x+x^2+x^7+x^8-2x^10-x^12)/((x+1)(x^2+1) (x^2+x+1) (x^2-x+1)(x^4-x^2+1)(x-1)^2), {x, 0, 90}], x] (* Harvey P. Dale, Oct 21 2011 *)

Prog

(PARI) Vec((1 + x + x^2 + x^7 + x^8 - 2*x^10 - x^12) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 - x^2 + x^4)) + O(x^100)) \\ Colin Barker, May 15 2019

Crossrefs

Sequence in context: A362960 A189635 A392305 * A058224 A131808 A196183

Adjacent sequences: A109782 A109783 A109784 * A109786 A109787 A109788

Keyword

nonn,easy

Author

Creighton Dement, Aug 14 2005

Status

approved