|
| |
|
|
A112553
|
|
Expansion of 1/( (1+x^2)*(1-x+x^2) ).
|
|
5
|
|
|
|
1, 1, -1, -2, 0, 2, 1, -1, -1, 0, 0, 0, 1, 1, -1, -2, 0, 2, 1, -1, -1, 0, 0, 0, 1, 1, -1, -2, 0, 2, 1, -1, -1, 0, 0, 0, 1, 1, -1, -2, 0, 2, 1, -1, -1, 0, 0, 0, 1, 1, -1, -2, 0, 2, 1, -1, -1, 0, 0, 0, 1, 1, -1, -2, 0, 2, 1, -1, -1, 0, 0, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,4
|
|
|
COMMENTS
|
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) = (1/4)*Sum_{k=0..n} (-1)^floor((n-k)/2)*Sum_{j=0..n} (1+(-1)^(n-j))*(1+(-1)^(j-k)) *binomial((j+k)/2, k).
a(n) = Sum_{k=0..n} (-1)^floor((n-k)/2)*((1 + (-1)^(n+k))/2)*binomial((n+k+2)/2, k+1).
a(n + 12) = a(n). (End)
|
|
|
EXAMPLE
|
G.f. = 1 + x - x^2 - 2*x^3 + 2*x^5 + x^6 - x^7 - x^8 + x^12 + x^13 - x^14 - 2*x^15 + ... - Michael Somos, Feb 15 2024
|
|
|
MATHEMATICA
|
Join[{1}, PadRight[{}, 120, {1, -1, -2, 0, 2, 1, -1, -1, 0, 0, 0, 1}]] (* G. C. Greubel, Jan 13 2022 *)
a[ n_] := {1, 1, -1, -2, 0, 2, 1, -1, -1, 0, 0, 0}[[1 + Mod[n, 12]]]; (* Michael Somos, Feb 15 2024 *)
|
|
|
PROG
|
(PARI) {a(n) = [1, 1, -1, -2, 0, 2, 1, -1, -1, 0, 0, 0][1 + n%12]}; /* Michael Somos, Feb 15 2024 */
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
easy,sign
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
