A274836 - OEIS

%I #10 May 15 2018 08:34:16

%S 1,1,1,1,2,3,4,9,18,33,89,215,481,1486,4187,10974,37907,121114,362953,

%T 1385575,4924557,16494655,68685792,268113185,990074770,4455129525,

%U 18896355932,76116156873,367577989487,1679905933299,7313571105815,37669220146964

%N Number of set partitions of [n] such that the difference between each element and its block index is a multiple of three.

%H Alois P. Heinz, <a href="/A274836/b274836.txt">Table of n, a(n) for n = 0..721</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

%e a(5) = 3: 14|25|3, 1|25|3|4, 1|2|3|4|5.

%e a(6) = 4: 14|25|36, 1|25|36|4, 1|2|36|4|5, 1|2|3|4|5|6.

%e a(7) = 9: 147|25|36, 14|25|36|7, 17|25|36|4, 1|25|36|47, 17|2|36|4|5, 1|2|36|47|5, 17|2|3|4|5|6, 1|2|3|47|5|6, 1|2|3|4|5|6|7.

%p b:= proc(n, m, t) option remember; `if`(n=0, 1,

%p      add(`if`(irem(j-t, 3)=0, b(n-1, max(m, j),

%p               irem(t+1, 3)), 0), j=1..m+1))

%p     end:

%p a:= n-> b(n, 0, 1):

%p seq(a(n), n=0..35);

%t b[n_, m_, t_] := b[n, m, t] = If[n == 0, 1, Sum[If[Mod[j-t, 3] == 0, b[n-1, Max[m, j], Mod[t+1, 3]], 0], {j, 1, m+1}]];

%t a[n_] := b[n, 0, 1];

%t Table[a[n], {n, 0, 35}] (* _Jean-François Alcover_, May 15 2018, after _Alois P. Heinz_ *)

%Y Column k=3 of A274835.

%K nonn

%O 0,5

%A _Alois P. Heinz_, Jul 08 2016