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%I #9 Oct 03 2023 02:02:19
%S 0,0,0,3,4,10,18,28,40,63,80,110,144,182,224,285,336,408,486,570,660,
%T 777,880,1012,1152,1300,1456,1647,1820,2030,2250,2480,2720,3003,3264,
%U 3570,3888,4218,4560,4953,5320,5740,6174,6622,7084,7605,8096,8648,9216,9800,10400
%N Sum of all the parts in the partitions of n into 3 positive integer parts.
%H Winston de Greef, <a href="/A350042/b350042.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = n * A069905(n).
%e 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.
%o (PARI) a(n) = floor((n^2+6)/12) * n \\ _Winston de Greef_, Oct 02 2023
%Y Cf. A069905.
%K nonn
%O 0,4
%A _Wesley Ivan Hurt_, Dec 10 2021
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