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)).
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).
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