A147652 Expansion of 1/(1 - x^4 - x^5 - x^6 + x^10).

1, 0, 0, 0, 1, 1, 1, 0, 1, 2, 2, 2, 2, 3, 4, 5, 5, 7, 8, 10, 12, 15, 18, 22, 26, 32, 40, 48, 58, 70, 86, 105, 128, 154, 188, 229, 279, 339, 412, 501, 610, 742, 902, 1098, 1335, 1624, 1975, 2403, 2923, 3556, 4324

Offset

0,10

Comments

Lim_{n->infinity} a(n)/a(n+1) = 0.8221036... (the smallest real root of 1 - x^4 - x^5 - x^6 + x^10). - Iain Fox, Nov 30 2017

Links

Iain Fox, Table of n, a(n) for n = 0..10000

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

Formula

G.f.: 1/(1 - x^4 - x^5 - x^6 + x^10).

a(n) = a(n-4) + a(n-5) + a(n-6) - a(n-10), n > 9. - Iain Fox, Nov 30 2017

Mathematica

CoefficientList[Series[1/(1-x^4-x^5-x^6+x^10), {x, 0, 50}], x] (* or *) LinearRecurrence[{0, 0, 0, 1, 1, 1, 0, 0, 0, -1}, {1, 0, 0, 0, 1, 1, 1, 0, 1, 2}, 60] (* Harvey P. Dale, Jun 24 2017 *)

Prog

(PARI) first(n) = Vec(1/(1 - x^4 - x^5 - x^6 + x^10) + O(x^n)) \\ Iain Fox, Nov 30 2017

Crossrefs

Sequence in context: A029101 A194815 A029080 * A058360 A241901 A238213

Adjacent sequences: A147649 A147650 A147651 * A147653 A147654 A147655

Keyword

nonn,easy

Author

Roger L. Bagula, Nov 09 2008

Extensions

Definition corrected by N. J. A. Sloane, Nov 10 2008

Status

approved