A174522 Expansion of 1/(1 - x - x^4 + x^6).

1, 1, 1, 1, 2, 3, 3, 3, 4, 6, 7, 7, 8, 11, 14, 15, 16, 20, 26, 30, 32, 37, 47, 57, 63, 70, 85, 105, 121, 134, 156, 191, 227, 256, 291, 348, 419, 484, 548, 640, 768, 904, 1033, 1189, 1409, 1673, 1938, 2223, 2599, 3083, 3612, 4162, 4823, 5683, 6696, 7775, 8986

Offset

0,5

Comments

Low limiting ratio in 100th iteration near 1.16663.

The polynomial is interesting for the puzzling low ratio and the Salem like root structure with two complex roots outside the unit circle.

Links

Table of n, a(n) for n=0..56.

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

Formula

a(n) = a(n-1) + a(n-4) + a(n-6). - Franck Maminirina Ramaharo, Oct 31 2018

Mathematica

CoefficientList[Series[1/(1 - x - x^4 + x^6), {x, 0, 60}], x]

Prog

(PARI) x='x+O('x^50); Vec(1/(1 - x - x^4 + x^6)) \\ G. C. Greubel, Nov 03 2018
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1 - x - x^4 + x^6))); // G. C. Greubel, Nov 03 2018

Crossrefs

Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.

Sequence in context: A351058 A036017 A029066 * A327719 A327716 A327720

Adjacent sequences: A174519 A174520 A174521 * A174523 A174524 A174525

Keyword

nonn,easy

Author

Roger L. Bagula, Nov 28 2010

Status

approved