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%I #51 Sep 02 2024 21:54:01
%S 1,1,0,0,1,3,9,17,108,324,1409,3807,13365,105764,347976,1825416,
%T 11309203,76330674,453496320,2638063039,19573857765,121970492469,
%U 939636604957,5944482289926,41069772211068,388012765239587,2642662404898875,21056674779654003
%N Number of partitions of [n] such that the element sum of each block is one more than a multiple of three.
%H Alois P. Heinz, <a href="/A374692/b374692.txt">Table of n, a(n) for n = 0..300</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%e a(0) = 1: the empty partition.
%e a(1) = 1: 1.
%e a(4) = 1: 1234.
%e a(5) = 3: 13|25|4, 1|235|4, 1|25|34.
%e a(6) = 9: 136|25|4, 13|256|4, 13|25|46, 16|235|4, 1|2356|4, 1|235|46, 16|25|34, 1|256|34, 1|25|346.
%e a(7) = 17: 1234567, 136|25|4|7, 13|256|4|7, 13|25|46|7, 13|25|4|67, 16|235|4|7, 1|2356|4|7, 1|235|46|7, 1|235|4|67, 16|25|34|7, 1|256|34|7, 1|25|346|7, 1|25|34|67, 16|25|37|4, 1|256|37|4, 1|25|367|4, 1|25|37|46.
%Y Column k=3 of A375924.
%Y Cf. A369079.
%K nonn
%O 0,6
%A _Alois P. Heinz_, Aug 31 2024