A175772 Expansion of 1/(1 - x - x^9 - x^17 + x^18).

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 16, 20, 25, 31, 38, 46, 55, 67, 81, 98, 119, 145, 177, 216, 263, 320, 389, 473, 575, 699, 850, 1034, 1258, 1530, 1862, 2265, 2755, 3351, 4076, 4958, 6031, 7336, 8923, 10854, 13203, 16060, 19535, 23762

Offset

0,10

Comments

The ratio a(n+1)/a(n) is 1.216391661138265... as n->infinity.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Michael Mossinghoff, Small Salem Numbers

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

Formula

G.f.: 1/((1 - x^2 + x^4)*(1 - x^4 - x^5 - x^6 + x^10)*(1 - x + x^2 - x^3 + x^4)).

a(n) = a(n-1) + a(n-9) + a(n-17) - a(n-18). - Harvey P. Dale, Jul 13 2014

Mathematica

CoefficientList[Series[1/(1 - x - x^9 - x^17 + x^18), {x, 0, 50}], x] (* or *)
LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11} , 60] (* Harvey P. Dale, Jul 13 2014 *)

Prog

(PARI) x='x+O('x^50); Vec(1/(1-x-x^9-x^17+x^18)) \\ G. C. Greubel, Nov 03 2018
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x-x^9-x^17+x^18))); // G. C. Greubel, Nov 03 2018

Crossrefs

Cf. A175739.

Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.

Sequence in context: A106801 A242417 A225657 * A124868 A165209 A072227

Adjacent sequences: A175769 A175770 A175771 * A175773 A175774 A175775

Keyword

nonn,easy

Author

Roger L. Bagula, Dec 04 2010

Status

approved