|
Search: id:A116503
|
|
|
| A116503 |
|
Sum of the areas of the Durfee squares of all partitions of n. |
|
+0
2
|
|
| 1, 2, 3, 8, 13, 26, 39, 64, 98, 148, 216, 322, 455, 648, 904, 1258, 1711, 2336, 3128, 4198, 5548, 7330, 9569, 12496, 16146, 20836, 26674, 34098, 43273, 54846, 69072, 86848, 108627, 135612, 168527, 209066, 258271, 318482, 391321, 479946, 586709
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
a(n)=sum(k^2*A115994(n,k),k=1..floor(sqrt(n))).
|
|
FORMULA
|
G.f.=sum(k^2*z^(k^2)/product((1-z^j)^2,j=1..k),k=1..infinity).
|
|
EXAMPLE
|
a(4)=8 because the partitions of 4, namely [4],[3,1],[2,2],[2,1,1], and [1,1,1,1], have Durfee squares of sizes 1,1,2,1, and 1, respectively, and 1^2+1^2+2^2+1^2+1^2=8.
|
|
MAPLE
|
g:=sum(k^2*z^(k^2)/product((1-z^j)^2, j=1..k), k=1..10): gser:=series(g, z=0, 52): seq(coeff(gser, z^n), n=1..45);
|
|
CROSSREFS
|
Cf. A115994, A115995.
Sequence in context: A002053 A102315 A004138 this_sequence A105204 A045692 A103196
Adjacent sequences: A116500 A116501 A116502 this_sequence A116504 A116505 A116506
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Emeric Deutsch, Vladeta Jovovic (vladeta(AT)Eunet.yu), Feb 18 2006
|
|
|
Search completed in 0.002 seconds
|
