A109609 Expansion of 1/((x-1)*(x+1)*(x^2+x+1)*(x^2+x-1)*(x^2-x+1)*(x^2+1)*(x^4-x^2+1)).

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 234, 378, 612, 990, 1602, 2592, 4194, 6786, 10980, 17766, 28746, 46512, 75259, 121771, 197030, 318801, 515831, 834632, 1350463, 2185095, 3535558, 5720653, 9256211, 14976864, 24233076, 39209940

Offset

0,3

Comments

FAMP Code for s batch of sequences satisfying the recurrence relation as (a(n)): A*B with A = - .25'i - .25i' - .25'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' - .25e, B = + 'i + i' + 'ji' + 'ki' + e. Sumtype is set to: sum[Y[15]]

Links

Table of n, a(n) for n=0..37.

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

Formula

a(0)=1, a(1)=1, a(2)=2, a(3)=3, a(4)=5, a(5)=8, a(6)=13, a(7)=21, a(8)=34, a(9)=55, a(10)=89, a(11)=144, a(12)=234, a(13)=378, a(n)=a(n-1)+ a(n-2)+ a(n-12)-a(n-13)-a(n-14). - Harvey P. Dale, Sep 20 2013

Maple

seriestolist(series(1/((x-1)*(x+1)*(x^2+x+1)*(x^2+x-1)*(x^2-x+1)*(x^2+1)*(x^4-x^2+1)), x=0, 40));

Mathematica

CoefficientList[Series[1/((x-1)(x+1)(x^2+x+1)(x^2+x-1)(x^2-x+1)(x^2+1)(x^4-x^2+1)), {x, 0, 40}], x] (* or *) LinearRecurrence[ {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1}, {1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 234, 378}, 40] (* Harvey P. Dale, Sep 20 2013 *)

Crossrefs

Cf. A000045.

Sequence in context: A177247 A069041 A177372 * A274162 A073958 A074317

Adjacent sequences: A109606 A109607 A109608 * A109610 A109611 A109612

Keyword

nonn

Author

Creighton Dement, Jul 31 2005

Status

approved