A275070 Number of set partitions of [n] such that i-j is a multiple of three for all i,j belonging to the same block.

1, 1, 1, 1, 2, 4, 8, 20, 50, 125, 375, 1125, 3375, 11700, 40560, 140608, 548912, 2142868, 8365427, 36140293, 156133187, 674526133, 3184194060, 15031429200, 70957944000, 362451121200, 1851389821260, 9456845543523, 51863510753775, 284431392616875

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..699

Wikipedia, Partition of a set

Formula

a(n) = Product_{i=0..2} A000110(floor((n+i)/3)).

Example

a(7) = 20: 147|25|36, 14|25|36|7, 147|25|3|6, 14|25|3|6|7, 147|2|36|5, 14|2|36|5|7, 147|2|3|5|6, 14|2|3|5|6|7, 17|25|36|4, 1|25|36|47, 1|25|36|4|7, 17|25|3|4|6, 1|25|3|47|6, 1|25|3|4|6|7, 17|2|36|4|5, 1|2|36|47|5, 1|2|36|4|5|7, 17|2|3|4|5|6, 1|2|3|47|5|6, 1|2|3|4|5|6|7.

Crossrefs

Column k=3 of A275069.

Cf. A000110.

Sequence in context: A121703 A301467 A358056 * A115219 A078160 A218088

Adjacent sequences: A275067 A275068 A275069 * A275071 A275072 A275073

Keyword

nonn

Author

Alois P. Heinz, Jul 15 2016

Status

approved