A104769 Expansion of g.f. -x/(1+x-x^3).

0, -1, 1, -1, 0, 1, -2, 2, -1, -1, 3, -4, 3, 0, -4, 7, -7, 3, 4, -11, 14, -10, -1, 15, -25, 24, -9, -16, 40, -49, 33, 7, -56, 89, -82, 26, 63, -145, 171, -108, -37, 208, -316, 279, -71, -245, 524, -595, 350, 174, -769, 1119, -945, 176, 943, -1888, 2064, -1121, -767, 2831, -3952

Offset: 0

Author

Creighton Dement, Mar 24 2005

Keywords

• sign
• easy
• less

Comments

Generating floretion is "jesright".

Pisano period lengths: 1, 7, 13, 14, 24, 91, 48, 28, 39, 168, 120, 182, 183, 336, 312, 56, 288, 273, 180, 168,.. (which differs from A104217 for example at index 23). - R. J. Mathar, Aug 10 2012

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10000
• Paul Barry, Centered polygon numbers, heptagons and nonagons, and the Robbins numbers, arXiv:2104.01644 [math.CO], 2021.
• Index entries for linear recurrences with constant coefficients, signature (-1,0,1).

Crossrefs

Apart from signs, essentially the same as A050935 and A078013.

Cf. A247917 (negative).

Cf. A000931, A057597.

Programs

Mathematica

LinearRecurrence[{-1, 0, 1}, {0, -1, 1}, 61] (* or *)
CoefficientList[Series[-x/(1 + x - x^3), {x, 0, 60}], x] (* Michael De Vlieger, Jul 02 2021 *)

PARI

a(n)=([0,1,0;0,0,1;1,0,-1]^n*[0;-1;1])[1,1] \\ Charles R Greathouse IV, Jun 11 2015

Formula

a(n) = -A247917(n-1).

Recurrence: a(n+3) = a(n) - a(n+2); a(0) = 0, a(1) = -1, a(2) = 1.

a(n+1) - a(n) = ((-1)^(n+1))*a(n+5).

a(n) = ((-1)^n)*A050935(n+1) = ((-1)^n)*A078013(n+2).

a(n) = A104771(n) - A104770(n).

Extensions

Edited by Ralf Stephan, Apr 05 2009