A374692 Number of partitions of [n] such that the element sum of each block is one more than a multiple of three.

1, 1, 0, 0, 1, 3, 9, 17, 108, 324, 1409, 3807, 13365, 105764, 347976, 1825416, 11309203, 76330674, 453496320, 2638063039, 19573857765, 121970492469, 939636604957, 5944482289926, 41069772211068, 388012765239587, 2642662404898875, 21056674779654003

Offset

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..300

Wikipedia, Partition of a set

Example

a(0) = 1: the empty partition.
a(1) = 1: 1.
a(4) = 1: 1234.
a(5) = 3: 13|25|4, 1|235|4, 1|25|34.
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.
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.

Crossrefs

Column k=3 of A375924.

Cf. A369079.

Sequence in context: A321869 A009211 A105538 * A056404 A056405 A009216

Adjacent sequences: A374689 A374690 A374691 * A374693 A374694 A374695

Keyword

nonn

Author

Alois P. Heinz, Aug 31 2024

Status

approved