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

Offset: 0

Author

Simon Plouffe

Keywords

• sign
• easy

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).

Crossrefs

Cf. A073011, A125950.

Programs

Magma

m:=50; R:=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

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 *)

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

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