A328824 Numerators of A113405(-n) (see the comment for details).

0, 1, 1, 1, -7, -7, -7, 57, 57, 57, -455, -455, -455, 3641, 3641, 3641, -29127, -29127, -29127, 233017, 233017, 233017, -1864135, -1864135, -1864135, 14913081, 14913081, 14913081, -119304647, -119304647, -119304647

Offset: 0

Author

Paul Curtz, Oct 28 2019

Keywords

• sign
• easy
• frac

Comments

Let A(n) = (2^n + (-1)^(n+1) - 2*sqrt(3)*sin((Pi*n)/3))/9. Then A(n) = A113405(n) and a(n) = numerator(A(-n)).

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,-8,8).

Crossrefs

Cf. A000079, A014990, A015565, A113405, A139818.

Programs

Maple

gf := x / ((1 - x)*(1 + 2*x)*(1 - 2*x + 4*x^2)): ser := series(gf, x, 36):
seq(coeff(ser,x,n),n=0..30); # Peter Luschny, Nov 11 2019

Mathematica

LinearRecurrence[{1,0,-8,8},{0,1,1,1},50] (* Paolo Xausa, Nov 13 2023 *)

PARI

concat(0, Vec(x / ((1 - x)*(1 + 2*x)*(1 - 2*x + 4*x^2)) + O(x^40))) \\ Colin Barker, Nov 11 2019

Formula

From Colin Barker, Nov 11 2019: (Start)

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

a(n) = a(n-1) - 8*a(n-3) + 8*a(n-4) for n>3. (End)