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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).
23
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
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
KEYWORD
sign,easy
AUTHOR
Roger L. Bagula, Nov 26 2010
STATUS
approved