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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, 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 (list; graph; refs; listen; history; text; internal format)
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: A102919 A102476 A302109 * A180380 A057420 A076049

Adjacent sequences:  A220483 A220484 A220485 * A220487 A220488 A220489

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Jan 18 2013

STATUS

approved

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Last modified March 19 23:02 EDT 2019. Contains 321343 sequences. (Running on oeis4.)