A143335 Expansion of (1 - 2*x^3 - x^4 - 2*x^5 - x^6 - x^7 - x^8 + 2*x^9)/(1 + x - x^3 - x^4 - x^5 - x^6 - x^7 + x^9 + x^10).

1, -1, 1, -2, 1, -2, 0, -1, -3, 2, -6, 1, -4, -3, -3, -5, -4, -7, -6, -9, -8, -14, -10, -18, -18, -20, -28, -27, -38, -39, -50, -57, -67, -79, -94, -109, -128, -154, -175, -213, -244, -292, -341, -400, -475, -553, -655, -768, -905, -1062, -1253, -1470, -1732

Offset

0,4

Comments

Shares the same 10th-order "Salem" linear recurrence with A029826, A173243 and A125950.

Links

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

Index entries for linear recurrences with constant coefficients, signature (-1,0,1,1,1,1,1,0,-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). - Franck Maminirina Ramaharo, Nov 02 2018

Maple

seq(coeff(series((1-2*x^3-x^4 -2*x^5-x^6-x^7-x^8+2*x^9)/(1+x-x^3-x^4-x^5-x^6-x^7 +x^9+x^10), x, n+1), x, n), n = 0..65); # G. C. Greubel, Mar 13 2020

Mathematica

LinearRecurrence[{-1, 0, 1, 1, 1, 1, 1, 0, -1, -1}, {1, -1, 1, -2, 1, -2, 0, -1, -3, 2}, 65] (* Franck Maminirina Ramaharo, Nov 02 2018 *)

Prog

(PARI) my(x='x+O('x^65)); Vec((1-2*x^3-x^4-2*x^5-x^6-x^7-x^8+2*x^9)/(1+x-x^3-x^4-x^5-x^6-x^7+x^9+x^10)) \\ G. C. Greubel, Nov 03 2018
(Magma) R<x>:=PowerSeriesRing(Integers(), 65); Coefficients(R!( (1-2*x^3-x^4 -2*x^5-x^6-x^7-x^8+2*x^9)/(1+x-x^3-x^4-x^5-x^6-x^7+x^9 +x^10) )); // G. C. Greubel, Nov 03 2018

Crossrefs

Cf. A029826, A070178, A087612, A107479, A107480, A109538.

Cf. A109543, A109544, A114749, A125950, A130844, A147851.

Sequence in context: A364835 A143352 A127170 * A099505 A156837 A255935

Adjacent sequences: A143332 A143333 A143334 * A143336 A143337 A143338

Keyword

sign,easy

Author

Roger L. Bagula and Gary W. Adamson, Oct 22 2008

Extensions

Edited by Assoc. Eds. of the OEIS - Jun 30 2010

Status

approved