|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
FORMULA
|
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):
|
|
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
|
|
|
STATUS
|
approved
|
|
|
|