A320555 Number of set partitions of [n] such that for each block b the smallest integer interval containing b has at most five elements and for at least one block c the smallest integer interval containing c has exactly five elements.

15, 64, 201, 585, 1741, 5375, 16355, 48601, 141921, 410425, 1182828, 3398411, 9728692, 27745449, 78861484, 223573925, 632578393, 1786856056, 5039984789, 14197033194, 39945491361, 112282665839, 315352029653, 885048266680, 2482371076351, 6958712870273

Offset

5,1

Links

Alois P. Heinz, Table of n, a(n) for n = 5..1000

Formula

a(n) = A276721(n) - A276720(n).

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)))(5):
seq(a(n), n=5..50);

Mathematica

b[n_, m_, l_List] := b[n, m, l] = If[n == 0, 1, Sum[b[n - 1, Max[m, j], Append[ReplacePart[l, 1 -> Nothing], If[j <= m, 0, j]]], {j, Append[l, m + 1]~Complement~{0}}]];
A[n_, k_] := If[n == 0, 1, If[k < 2, k, b[n, 0, Array[0 &, k - 1]]]];
a[n_] := With[{k = 5}, A[n, k] - If[k == 0, 0, A[n, k - 1]]];
a /@ Range[5, 35] (* Jean-François Alcover, Dec 08 2020, after Alois P. Heinz *)

Crossrefs

Column k=5 of A276727.

Cf. A276720, A276721, A320618.

Sequence in context: A044153 A044534 A063483 * A347478 A082825 A274444

Adjacent sequences: A320552 A320553 A320554 * A320556 A320557 A320558

Keyword

nonn,easy

Author

Alois P. Heinz, Oct 15 2018

Status

approved