A225396 Expansion of 1/(1 - x - x^2 + x^10 - x^12).

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 88, 142, 229, 369, 595, 959, 1546, 2492, 4017, 6475, 10438, 16826, 27123, 43722, 70479, 113611, 183139, 295217, 475885, 767119, 1236583, 1993351, 3213249, 5179704, 8349597, 13459412, 21696349, 34974155, 56377758, 90880011

Offset

0,3

Comments

Limiting ratio is 1.61198..., the largest real root of -1 + x^2 - x^10 - x^11 + x^12 = 0.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Roger L. Bagula, Demo file

Index entries for linear recurrences with constant coefficients, signature (1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 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)=88, a(11)=142, a(n)=a(n-1)+a(n-2)- a(n-10)+ a(n-12). - Harvey P. Dale, Apr 12 2014

Mathematica

CoefficientList[Series[1/(1 - x - x^2 + x^10 - x^12), {x, 0, 50}], x]
LinearRecurrence[{1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1}, {1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 88, 142}, 50] (* Harvey P. Dale, Apr 12 2014 *)

Crossrefs

Cf. A117791, A107293, A204631, A225393, A225394, A029826, A147660.

Sequence in context: A206139 A374765 A023440 * A290689 A191869 A077373

Adjacent sequences: A225393 A225394 A225395 * A225397 A225398 A225399

Keyword

nonn,easy

Author

Roger L. Bagula, May 06 2013

Status

approved