A109610 Expansion of (1+3*x^4-2*x^7+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, 1, 1, 1, 4, 4, 4, 2, 2, 2, 3, 3, 3, 3, 3, 3, 6, 6, 6, 4, 4, 4, 5, 5, 5, 5, 5, 5, 8, 8, 8, 6, 6, 6, 7, 7, 7, 7, 7, 7, 10, 10, 10, 8, 8, 8, 9, 9, 9, 9, 9, 9, 12, 12, 12, 10, 10, 10, 11, 11, 11, 11, 11, 11, 14, 14, 14, 12, 12, 12, 13, 13, 13, 13, 13, 13, 16, 16, 16, 14, 14, 14, 15, 15, 15, 15

Offset

0,5

Links

Table of n, a(n) for n=0..85.

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

Formula

a(0)=1, a(1)=1, a(2)=1, a(3)=1, a(4)=4, a(5)=4, a(6)=4, a(7)=2, a(8)=2, a(9)=2, a(10)=3, a(11)=3, a(12)=3, a(n)=a(n-1)+a(n-12)-a(n-13). - Harvey P. Dale, Aug 19 2015

Maple

seriestolist(series((1+3*x^4-2*x^7+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), x=0, 150)); -or- Floretion Algebra Multiplication Program, FAMP Code: 4baseisumseq[ .25'i + .25i' + .25'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' + .25e]. Sumtype is set to: sum[Y[15]] = sum[ * ]

Mathematica

CoefficientList[Series[(1+3x^4-2x^7+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), {x, 0, 100}], x] (* or *) LinearRecurrence[ {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {1, 1, 1, 1, 4, 4, 4, 2, 2, 2, 3, 3, 3}, 100] (* Harvey P. Dale, Aug 19 2015 *)

Crossrefs

Sequence in context: A201941 A180060 A220668 * A067395 A213274 A182565

Adjacent sequences: A109607 A109608 A109609 * A109611 A109612 A109613

Keyword

nonn

Author

Creighton Dement, Jul 31 2005

Status

approved