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A350042
Sum of all the parts in the partitions of n into 3 positive integer parts.
2
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
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Dec 10 2021
STATUS
approved