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
Keywords
Examples
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.
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)).