A116928 Number of 1's in all self-conjugate partitions of n.

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

Offset

1,5

Comments

a(n)=Sum(k*A116927(n,k), k>=0).

Links

Table of n, a(n) for n=1..62.

Formula

G.f.=x+sum(x^(k^2+2)/(1-x^2)/product(1-x^(2j), j=1..k), k=1..infinity).

a(n) = A096911(n)-(1+(-1)^n)/2, m>1. - Vladeta Jovovic, Feb 27 2006

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

Cf. A116927.

Sequence in context: A100927 A001687 A159072 * A239948 A034391 A239243

Adjacent sequences: A116925 A116926 A116927 * A116929 A116930 A116931

Keyword

nonn

Author

Emeric Deutsch, Feb 26 2006

Status

approved