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A328824
Numerators of A113405(-n) (see the comment for details).
1
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
0,5
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)).
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)
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 *)
PROG
(PARI) concat(0, Vec(x / ((1 - x)*(1 + 2*x)*(1 - 2*x + 4*x^2)) + O(x^40))) \\ Colin Barker, Nov 11 2019
CROSSREFS
KEYWORD
sign,easy,frac
AUTHOR
Paul Curtz, Oct 28 2019
STATUS
approved