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A029826

Expansion of 1/(x^10+x^9-x^7-x^6-x^5-x^4-x^3+x+1) (inverse of Salem polynomial).

1, -1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 2, 1, 2, 3, 2, 4, 3, 5, 5, 6, 8, 8, 10, 12, 14, 16, 20, 22, 27, 31, 37, 44, 50, 61, 70, 83, 98, 115, 135, 159, 187, 220, 259, 304, 359, 420, 496, 583, 685, 807, 948, 1116, 1312, 1544

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OFFSET

0,14

COMMENTS

The root 1.1762808182599175065440703384740350... is the smallest known Salem number (A073011).

LINKS

Simon Plouffe, Table of n, a(n) for n = 0..2998

Leonard Lewin, Structural Properties of Polylogarithms, AMS #37. p. 365, 1991.

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

FORMULA

a(n) = -a(n-1) + a(n-3) + a(n-4) + a(n-5) + a(n-6) + a(n-7) - a(n-9) - a(n-10). - Roger L. Bagula and Gary W. Adamson, Oct 23 2008

MATHEMATICA

LinearRecurrence[{-1, 0, 1, 1, 1, 1, 1, 0, -1, -1}, {1, -1, 1, 0, 0, 1, 0, 1, 0, 1}, 100] (* G. C. Greubel, May 07 2018 *)

CoefficientList[Series[1/(x^10+x^9-x^7-x^6-x^5-x^4-x^3+x+1), {x, 0, 60}], x] (* Harvey P. Dale, Mar 07 2026 *)

PROG

(PARI) Vec(1/(x^10+x^9-x^7-x^6-x^5-x^4-x^3+x+1)+O(x^66)) \\ Joerg Arndt, May 01 2018

(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(x^10+x^9-x^7-x^6-x^5-x^4-x^3+x+1))); // G. C. Greubel, May 07 2018

CROSSREFS

Cf. A073011, A125950.

Sequence in context: A071283 A172986 A364642 * A192185 A246833 A213624

Adjacent sequences: A029823 A029824 A029825 * A029827 A029828 A029829

KEYWORD

sign,easy

AUTHOR

Simon Plouffe

STATUS

approved

URL: https://oeis.org/A029826

⇱ A029826 - OEIS