A220486 a(n) = n(p(n)-d(n)): sum of all of parts of all partitions of n with at least one distinct part.

0, 0, 3, 8, 25, 42, 91, 144, 243, 380, 594, 852, 1287, 1834, 2580, 3616, 5015, 6822, 9272, 12420, 16548, 21956, 28819, 37608, 48875, 63232, 81162, 103936, 132327, 167880, 212040, 266976, 334587, 418404, 520765, 646848, 800495, 988418, 1216059, 1493200

Offset

1,3

Links

Table of n, a(n) for n=1..40.

Formula

a(n) = n*(A000041(n) - A000005(n)) = A066186(n) - A038040(n) = n*A144300(n).

Example

For n = 6
-----------------------------------------------------
Partitions of 6            Value
-----------------------------------------------------
6 .......................... 0  (all parts are equal)
5 + 1 ...................... 6
4 + 2 ...................... 6
4 + 1 + 1 .................. 6
3 + 3 ...................... 0  (all parts are equal)
3 + 2 + 1 .................. 6
3 + 1 + 1 + 1 .............. 6
2 + 2 + 2 .................. 0  (all parts are equal)
2 + 2 + 1 + 1 .............. 6
2 + 1 + 1 + 1 + 1 .......... 6
1 + 1 + 1 + 1 + 1 + 1 ...... 0  (all parts are equal)
-----------------------------------------------------
The sum of the values is    42
On the other hand p(6) = A000041(6) = 11 and d(6) = A000005(6) = 4, so a(6) = 6*(p(6) - d(6)) = 6*(11 - 4) = 6*7 = 42.

Crossrefs

Cf. A000005, A000041, A038040, A066186, A144300, A220477.

Sequence in context: A348418 A302109 A328272 * A180380 A057420 A076049

Adjacent sequences: A220483 A220484 A220485 * A220487 A220488 A220489

Keyword

nonn,easy

Author

Omar E. Pol, Jan 18 2013

Status

approved