A143478 Expansion of 1/(x^10*p(1/x)), where p(x) = x^11 + x^10 - 11*x^9 - 11*x^8 + 42*x^7 + 40*x^6 - 66*x^5 - 54*x^4 + 42*x^3 + 24*x^2 - 8*x - 1 is a Salem polynomial.

0, 1, -1, 12, -12, 91, -89, 560, -526, 3061, -2715, 15526, -12779, 74893, -56092, 348808, -232184, 1584273, -909357, 7065982, -3354913, 31100725, -11473678, 135587365, -34883109, 587116592, -82703752, 2530527727, -52581912, 10874166572, 1107267567, 46648306254

Offset

0,4

Links

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

Index entries for linear recurrences with constant coefficients, signature (-1,11,11,-42,-40,66,54,-42,-24,8,1).

Formula

G.f.: x/(1 + x - 11*x^2 - 11*x^3 + 42*x^4 + 40*x^5 - 66*x^6 - 54*x^7 + 42*x^8 + 24*x^9 - 8*x^10 - x^11).

a(n) = -a(n-1) + 11*a(n-2) + 11*a(n-3) - 42*a(n-4) - 40*a(n-5) + 66*a(n-6) + 54*a(n-7) - 42*a(n-8) - 24*a(n-9) + 8*a(n-10) + a(n-11). - Franck Maminirina Ramaharo, Nov 02 2018

Mathematica

CoefficientList[Series[x/(1 + x - 11*x^2 - 11*x^3 + 42*x^4 + 40*x^5 - 66*x^6 - 54*x^7 + 42*x^8 + 24*x^9 - 8*x^10 - x^11), {x, 0, 30}], x]

Prog

(PARI) x='x+O('x^50); concat([0], Vec(x/(1+x-11*x^2-11*x^3+42*x^4+40*x^5 -66*x^6-54*x^7+42*x^8+24*x^9-8*x^10-x^11))) \\ G. C. Greubel, Nov 03 2018
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(x/(1+x-11*x^2-11*x^3+42*x^4+40*x^5-66*x^6-54*x^7+42*x^8 +24*x^9-8*x^10-x^11))); // G. C. Greubel, Nov 03 2018

Crossrefs

Cf. A143471, A167603.

Sequence in context: A328531 A111306 A151777 * A219400 A219448 A067123

Adjacent sequences: A143475 A143476 A143477 * A143479 A143480 A143481

Keyword

easy,sign

Author

Roger L. Bagula and Gary W. Adamson, Oct 24 2008

Extensions

Edited, new name, and offset corrected by Franck Maminirina Ramaharo, Nov 02 2018

Status

approved