A173908 Expansion of 1/(1 + x - x^3 - x^4 - x^8 - x^12 - x^13 - x^17 - x^21 - x^22 - x^26 - x^30 - x^31 + x^33 + x^34).

1, -1, 1, 0, 0, 0, 1, -1, 2, -2, 3, -2, 3, -2, 4, -3, 6, -5, 9, -7, 12, -9, 16, -12, 22, -17, 31, -24, 43, -33, 59, -45, 81, -63, 113, -88, 156, -121, 215, -168, 298, -233, 412, -323, 570, -448, 788, -621, 1090, -861, 1507, -1193, 2084, -1654, 2882, -2293

Offset

0,9

Comments

This polynomial is what I call a bi-Salem polynomial because it has two roots bigger than 1 (one positive and one negative).

Links

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

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

Formula

a(n) = a(n-1) + (n-3) + a(n-4) + a(n-8) + a(n-12) + a(n-13) + a(n-17) + a(n-21) + a(n-22) + a(n-26) + a(n-30) + a(n-31) - a(n-33) - a(n-34). - Franck Maminirina Ramaharo, Nov 02 2018

Maple

seq(coeff(series(1/(1+x-x^3-x^4-x^8-x^12-x^13-x^17-x^21-x^22-x^26-x^30-x^31+ x^33+x^34), x, n+1), x, n), n = 0..60); # G. C. Greubel, Dec 15 2019

Mathematica

CoefficientList[Series[1/(1+x-x^3-x^4-x^8-x^12-x^13-x^17-x^21-x^22-x^26-x^30 - x^31+x^33+x^34), {x, 0, 60}], x]

Prog

(PARI) x='x+O('x^60); Vec(1/(1+x-x^3-x^4-x^8-x^12-x^13-x^17-x^21-x^22-x^26 - x^30-x^31+x^33+x^34)) \\ G. C. Greubel, Nov 03 2018
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1+x-x^3 -x^4-x^8-x^12-x^13-x^17-x^21-x^22-x^26-x^30-x^31+x^33+x^34))); // G. C. Greubel, Nov 03 2018
(Sage)
def A173908_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/(1+x-x^3-x^4-x^8-x^12-x^13-x^17-x^21-x^22-x^26-x^30 - x^31+x^33+x^34) ).list()
A173908_list(30) # G. C. Greubel, Dec 15 2019

Crossrefs

Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.

Sequence in context: A350067 A308450 A229123 * A329045 A329345 A054030

Adjacent sequences: A173905 A173906 A173907 * A173909 A173910 A173911

Keyword

sign,easy

Author

Roger L. Bagula, Nov 26 2010

Status

approved