|
|
A116928
|
|
Number of 1's in all self-conjugate partitions of n.
|
|
1
|
|
|
1, 0, 1, 0, 2, 1, 3, 2, 4, 4, 6, 6, 8, 9, 11, 12, 15, 17, 20, 22, 26, 29, 34, 37, 43, 48, 55, 60, 69, 76, 86, 94, 106, 117, 131, 143, 160, 176, 195, 213, 236, 259, 285, 311, 342, 374, 410, 446, 488, 533, 581, 631, 688, 748, 813, 881, 957, 1038, 1125, 1216, 1317, 1425
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,5
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
G.f.=x+sum(x^(k^2+2)/(1-x^2)/product(1-x^(2j), j=1..k), k=1..infinity).
|
|
EXAMPLE
|
a(12)=6 because the self-conjugate partitions of 12 are [6,2,1,1,1,1],[5,3,2,1,1] and [4,4,2,2], containing a total of six 1's.
|
|
MAPLE
|
f:=x+sum(x^(k^2+2)/(1-x^2)/product(1-x^(2*j), j=1..k), k=1..10): fser:=series(f, x=0, 70): seq(coeff(fser, x^n), n=1..67);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|