A350042 Sum of all the parts in the partitions of n into 3 positive integer parts.

0, 0, 0, 3, 4, 10, 18, 28, 40, 63, 80, 110, 144, 182, 224, 285, 336, 408, 486, 570, 660, 777, 880, 1012, 1152, 1300, 1456, 1647, 1820, 2030, 2250, 2480, 2720, 3003, 3264, 3570, 3888, 4218, 4560, 4953, 5320, 5740, 6174, 6622, 7084, 7605, 8096, 8648, 9216, 9800, 10400

Offset

0,4

Links

Winston de Greef, Table of n, a(n) for n = 0..10000

Index entries for sequences related to partitions

Formula

a(n) = n * A069905(n).

Example

a(9) = 63 since we have the partitions (1,1,7), (1,2,6), (1,3,5), (1,4,4), (2,2,5), (2,3,4) and (3,3,3). Since the parts in each partition sum to 9 and we have 7 partitions, a(9) = 9*7 = 63.

Prog

(PARI) a(n) = floor((n^2+6)/12) * n \\ Winston de Greef, Oct 02 2023

Crossrefs

Cf. A069905.

Sequence in context: A034775 A280246 A338012 * A006490 A307856 A171160

Adjacent sequences: A350039 A350040 A350041 * A350043 A350044 A350045

Keyword

nonn

Author

Wesley Ivan Hurt, Dec 10 2021

Status

approved