|
|
A134172
|
|
Expansion of x^2*(1+x)*(1-x+x^2) / ((1-x)^2*(1+x^2)^2).
|
|
2
|
|
|
0, 0, 1, 2, 1, 1, 4, 5, 2, 2, 7, 8, 3, 3, 10, 11, 4, 4, 13, 14, 5, 5, 16, 17, 6, 6, 19, 20, 7, 7, 22, 23, 8, 8, 25, 26, 9, 9, 28, 29, 10, 10, 31, 32, 11, 11, 34, 35, 12, 12, 37, 38, 13, 13, 40, 41, 14, 14, 43, 44, 15, 15, 46, 47, 16, 16, 49, 50, 17, 17, 52, 53, 18, 18, 55, 56, 19, 19, 58
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
Old definition was: "Starting with 0, 1, 2, 3, ... (A001477), write 0, 0 instead of a(0), 1, 1 instead of a(3) and in general n, n instead of a(3n)".
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x^2*(1+x)*(1-x+x^2) / ((1-x)^2*(1+x^2)^2).
a(n) = (-2+(-i)^n+i^n+(4-(1+i)*(-i)^n-(1-i)*i^n)*n)/8 where i = sqrt(-1).
a(n) = 2*a(n-1)-3*a(n-2)+4*a(n-3)-3*a(n-4)+2*a(n-5)-a(n-6) for n>5. (End)
|
|
MATHEMATICA
|
LinearRecurrence[{2, -3, 4, -3, 2, -1}, {0, 0, 1, 2, 1, 1}, 50] (* G. C. Greubel, May 29 2016 *)
|
|
PROG
|
(PARI) concat(vector(2), Vec(x^2*(1+x)*(1-x+x^2)/((1-x)^2*(1+x^2)^2) + O(x^50))) \\ Colin Barker, May 30 2016
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|