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

Author

Wesley Ivan Hurt, Dec 10 2021

Keywords

• nonn

Examples

			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.
		

Links

• Winston de Greef, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to partitions

Crossrefs

Cf. A069905.

Programs

PARI

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

Formula

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