A199933 Trisection 0 of A199744.

1, 1, -4, 0, 20, -25, -71, 216, 94, -1220, 1037, 4941, -11440, -11008, 72112, -33453, -326675, 577060, 950750, -4129272, 279257, 20740793, -27217100, -72078336, 228625372, 83808415, -1271796511, 1153458144, 5060707454, -12183603100, -10694679515, 75519944325, -39290857304, -336819940736

Offset: 0

Author

N. J. A. Sloane, Nov 12 2011

Keywords

• sign
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Hirschhorn, Michael D., Non-trivial intertwined second-order recurrence relations, Fibonacci Quart. 43 (2005), no. 4, 316-325. See p. 324.
• Index entries for linear recurrences with constant coefficients, signature (-1,-5,1,-1).

Programs

Mathematica

CoefficientList[ Series[(1 +2x +2x^2)/(1 +x +5x^2 -x^3 +x^4), {x, 0, 33}], x] (* or *)
LinearRecurrence[{-1, -5, 1, -1}, {1, 1, -4, 0}, 33] (* Robert G. Wilson v, Dec 27 2017 *)

PARI

Vec((1 + 2*x + 2*x^2) / (1 + x + 5*x^2 - x^3 + x^4) + O(x^40)) \\ Colin Barker, Dec 27 2017

Formula

From Colin Barker, Dec 27 2017: (Start)

G.f.: (1 + 2*x + 2*x^2) / (1 + x + 5*x^2 - x^3 + x^4).

a(n) = -a(n-1) - 5*a(n-2) + a(n-3) - a(n-4) for n>3.

(End)