A175782 -id:A175782 - cp's OEIS frontend

A175773 Expansion of 1/(1 - x - x^6 - x^11 + x^12).

1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 8, 10, 13, 17, 22, 28, 37, 48, 62, 80, 103, 133, 172, 223, 289, 374, 483, 625, 808, 1045, 1352, 1749, 2262, 2926, 3785, 4896, 6333, 8191, 10595, 13704, 17726, 22929, 29659, 38363, 49622, 64185, 83022, 107388, 138905, 179672

Offset: 0

Roger L. Bagula, Dec 04 2010

The ratio a(n+1)/a(n) is 1.2934859531254534... for n->infinity.

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 (1,0,0,0,0,1,0,0,0,0,1,-1).

Cf. A175739.

Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x-x^6-x^11+x^12))); // G. C. Greubel, Nov 03 2018

CoefficientList[Series[1/(1 - x - x^6 - x^11 + x^12), {x, 0, 50}], x]

x='x+O('x^50); Vec(1/(1-x-x^6-x^11+x^12)) \\ G. C. Greubel, Nov 03 2018

G.f.: 1/((1 - x + x^2)*(1 - x^2 - x^3 + x^5 - x^7 - x^8 + x^10)).

a(n) = a(n-1) + a(n-6) + a(n-11) - a(n-12), n >= 12. - Franck Maminirina Ramaharo, Oct 31 2018

A181600 Expansion of 1/(1 - x - x^2 + x^8 - x^10).

Original entry on oeis.org

1, 1, 2, 3, 5, 8, 13, 21, 33, 53, 85, 136, 218, 349, 559, 895, 1434, 2297, 3679, 5893, 9439, 15119, 24217, 38790, 62132, 99520, 159407, 255331, 408978, 655083, 1049283, 1680695, 2692063, 4312028, 6906816, 11063033, 17720278, 28383559, 45463532, 72821479

Offset: 0

Roger L. Bagula, May 06 2013

Limiting ratio is 1.60176..., the largest real root of -1 + x^2 - x^8 - x^9 + x^10. Compare this constant to Lehmer's Salem constant A073011 and the golden mean.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,0,0,0,-1,0,1).

Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A204631, A225391, A225393, A225394, A225482, A225499.

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1 -x-x^2+x^8-x^10))); // G. C. Greubel, Nov 03 2018

CoefficientList[Series[1/(1 - x - x^2 + x^8 - x^10), {x, 0, 50}], x]
LinearRecurrence[{1, 1, 0, 0, 0, 0, 0, -1, 0, 1}, {1, 1, 2, 3, 5, 8, 13, 21, 33, 53}, 50] (* Harvey P. Dale, Aug 11 2015 *)

Vec(1/(1 -x -x^2 +x^8 -x^10) + O(x^50)) \\ G. C. Greubel, Nov 16 2016

a(n) = a(n-1) + a(n-2) - a(n-8) + a(n-10). - Franck Maminirina Ramaharo, Oct 31 2018

cp's OEIS Frontend

A175773 Expansion of 1/(1 - x - x^6 - x^11 + x^12).

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