A143075 Polynomial expansion sequence: p(x)=1/(1 - 4x + 5x^2 - 6x^4 + 6x^5 - x^6 - 2x^7 + x^8).

1, 4, 11, 24, 47, 86, 152, 262, 444, 742, 1228, 2018, 3301, 5382, 8755, 14218, 23063, 37380, 60552, 98052, 158736, 256932, 415824, 672924, 1088929, 1762048, 2851187, 4613460, 7464887, 12078602, 19543760

Offset

1,2

Comments

Ratio limit is the golden mean.

Links

Table of n, a(n) for n=1..31.

Formula

a(n) = expansion(1/(1 - 4x + 5x^2 - 6x^4 + 6x^5 - x^6 - 2x^7 + x^8))

Mathematica

Clear[p, q, x, n, a]; p[x_] = Expand[((x^2 - x - 1)*(x^2 - 1)*(x^2 - 2*x + 1)*(x^2 - x + 1)) ]; q[x_] = ExpandAll[1/(x^8*p[1/x])]; a = Table[SeriesCoefficient[Series[q[x], {x, 0, 30}], n], {n, 0, 30}]
CoefficientList[Series[1/(1-4x+5x^2-6x^4+6x^5-x^6-2x^7+x^8), {x, 0, 30}], x]  (* Harvey P. Dale, Apr 06 2011 *)

Crossrefs

Sequence in context: A001752 A160860 A192748 * A290707 A322618 A260057

Adjacent sequences: A143072 A143073 A143074 * A143076 A143077 A143078

Keyword

nonn,uned

Author

Roger L. Bagula, Oct 13 2008

Status

approved