

A067619


Total number of parts in all selfconjugate partitions of n. Also, sum of largest parts of all selfconjugate partitions of n.


4



0, 1, 0, 2, 2, 3, 3, 4, 7, 8, 9, 10, 15, 16, 18, 23, 30, 32, 35, 42, 51, 59, 63, 73, 89, 100, 106, 125, 145, 160, 174, 198, 229, 255, 274, 310, 355, 388, 420, 472, 534, 582, 631, 701, 784, 859, 928, 1021, 1144, 1243, 1338, 1475, 1630, 1767, 1909, 2089, 2299
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,4


REFERENCES

Knopfmacher, Arnold and Robbins, Neville, Identities for the total number of parts in partitions of integers. Util. Math. 67 (2005), 918.


LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000


FORMULA

G.f.: Sum for n>=1 of n q^(2n1) (1+q) (1+q^3) ... (1+q^(2n3)).


MATHEMATICA

CoefficientList[Series[Sum[n*q^(2n1)*Product[1+q^k, {k, 1, 2n3, 2}], {n, 1, 30}], {q, 0, 60}], q]


CROSSREFS

Cf. A000700, A000701, A006128, A015723, A046682, A079499.
Sequence in context: A241152 A164529 A153906 * A236972 A184351 A146922
Adjacent sequences: A067616 A067617 A067618 * A067620 A067621 A067622


KEYWORD

easy,nonn


AUTHOR

Naohiro Nomoto, Feb 01 2002


EXTENSIONS

Edited by Dean Hickerson, Feb 11 2002


STATUS

approved



