A317806 Number of set partitions of [k] into 4 blocks with equal element sum, where k is the n-th positive integer that allows such a partition.

1, 1, 871, 2650, 9462094, 31650271, 171019406993, 595828948333, 4107584704538352, 14702365152800667, 118513210888679225825, 432046935173440593804, 3881432331405193485285518, 14337098117309087488187476, 139477762791757859249400365738, 520312171172086830267314753894

Offset

1,3

Comments

k = 7, 8, 15, 16, 23, ... A047521(n+1) for n = 1, 2, 3, 4, 5, ... .

Links

Table of n, a(n) for n=1..16.

Wikipedia, Partition of a set

Formula

a(n) = A275714(A047521(n+1),4).

Example

a(1) = 1: 16|25|34|7 with k = 7.
a(2) = 1: 18|27|36|45 with k = 8.

Maple

b:= proc() option remember; local i, j, t; `if`(args[1]=0,
      `if`(nargs=2, 1, b(args[t] $t=2..nargs)), add(
      `if`(args[j] -args[nargs]<0, 0, b(sort([seq(args[i]-
      `if`(i=j, args[nargs], 0), i=1..nargs-1)])[],
                args[nargs]-1)), j=1..nargs-1))
    end:
a:= proc(n) option remember; (k-> (m->
      b((m/4)$4, k)/24)(k*(k+1)/2))(4*n+3/2*(1-(-1)^n))
    end:
seq(a(n), n=1..8);

Crossrefs

Cf. A047521, A275714.

Sequence in context: A206172 A205426 A035855 * A031783 A253167 A214285

Adjacent sequences: A317803 A317804 A317805 * A317807 A317808 A317809

Keyword

nonn

Author

Alois P. Heinz, Aug 07 2018

Status

approved