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A173911 Expansion of 1/(1 - x + x^2 - x^3 - x^6 + x^7 - x^8 + x^9 - x^10 + x^11 - x^12 -x^15 + x^16 - x^17 + x^18). 24
1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 6, 7, 8, 10, 12, 14, 16, 19, 23, 28, 33, 39, 46, 55, 66, 78, 92, 110, 131, 155, 184, 219, 260, 309, 368, 437, 519, 617, 733, 871, 1036, 1231, 1462, 1737, 2065, 2454, 2916, 3465, 4118, 4894, 5816, 6911, 8213 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

COMMENTS

Second lowest Salem number polynomial expansion sequence.

Limiting ratio is 1.188368147508223588142960958629.

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

FORMULA

a(n) = a(n-1) - a(n-2) + a(n-3) + a(n-6) - a(n-7) + a(n-8) - a(n-9) + a(n-10) - a(n-11) + a(n-12) + a(n-15) - a(n-16) + a(n-17) - a(n-16). - Franck Maminirina Ramaharo, Nov 02 2018

MAPLE

seq(coeff(series(1/(1-x+x^2-x^3-x^6+x^7-x^8+x^9-x^10+x^11-x^12-x^15+x^16 -x^17+x^18), x, n+1), x, n), n = 0..50); # G. C. Greubel, Dec 15 2019

MATHEMATICA

CoefficientList[Series[1/(1-x+x^2-x^3-x^6+x^7-x^8+x^9-x^10+x^11-x^12-x^15+x^16 -x^17+x^18), {x, 0, 50}], x]

PROG

(PARI) my(x='x+O('x^50)); Vec(1/(1-x+x^2-x^3-x^6+x^7-x^8+x^9-x^10+x^11-x^12-x^15+ x^16-x^17+x^18)) \\ G. C. Greubel, Nov 03 2018

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!(1/(1-x+x^2-x^3-x^6+x^7-x^8+x^9-x^10+x^11-x^12-x^15+x^16-x^17+x^18))); // G. C. Greubel, Nov 03 2018

(Sage)

def A173911_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P( 1/(1-x+x^2-x^3-x^6+x^7-x^8+x^9-x^10+x^11-x^12-x^15+x^16 -x^17+x^18) ).list()

A173911_list(50) # G. C. Greubel, Dec 15 2019

CROSSREFS

Cf. A167289.

Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.

Sequence in context: A131795 A035382 A094988 * A076269 A143644 A104410

Adjacent sequences:  A173908 A173909 A173910 * A173912 A173913 A173914

KEYWORD

nonn,easy

AUTHOR

Roger L. Bagula, Nov 26 2010

STATUS

approved

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Last modified September 27 03:21 EDT 2020. Contains 337380 sequences. (Running on oeis4.)