A320556 Number of set partitions of [n] such that for each block b the smallest integer interval containing b has at most six elements and for at least one block c the smallest integer interval containing c has exactly six elements.

52, 265, 966, 3172, 10100, 32918, 111138, 373888, 1238236, 4034221, 12991481, 41567855, 132719006, 423099220, 1346053178, 4271656023, 13520858094, 42696919677, 134582517515, 423599583268, 1331701708711, 4182193622677, 13121508724973, 41131777789545

Offset: 6

Author

Alois P. Heinz, Oct 15 2018

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..1000

Crossrefs

Column k=6 of A276727.

Cf. A276721, A276722, A320619.

Programs

Maple

b:= proc(n, m, l) option remember; `if`(n=0, 1,
      add(b(n-1, max(m, j), [subsop(1=NULL, l)[],
      `if`(j<=m, 0, j)]), j={l[], m+1} minus {0}))
    end:
A:= (n, k)-> `if`(n=0, 1, `if`(k<2, k, b(n, 0, [0$(k-1)]))):
a:= n-> (k-> A(n, k) -`if`(k=0, 0, A(n, k-1)))(6):
seq(a(n), n=6..50);

Formula

a(n) = A276722(n) - A276721(n).