A320558 Number of set partitions of [n] such that for each block b the smallest integer interval containing b has at most eight elements and for at least one block c the smallest integer interval containing c has exactly eight elements.

877, 5852, 27267, 110545, 422396, 1578192, 5877165, 22355618, 87597223, 345223398, 1352883364, 5249340393, 20158426185, 76729396494, 290259302392, 1094289866107, 4121529511428, 15518374075986, 58402401729381, 219602989556557, 824720185307142, 3092742982300231

Offset: 8

Author

Alois P. Heinz, Oct 15 2018

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..1000

Crossrefs

Column k=8 of A276727.

Cf. A276723, A276724, A320621.

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)))(8):
seq(a(n), n=8..50);

Formula

a(n) = A276724(n) - A276723(n).