cp's OEIS Frontend

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.

%I A317806 #12 Nov 02 2018 09:07:53
%S A317806 1,1,871,2650,9462094,31650271,171019406993,595828948333,
%T A317806 4107584704538352,14702365152800667,118513210888679225825,
%U A317806 432046935173440593804,3881432331405193485285518,14337098117309087488187476,139477762791757859249400365738,520312171172086830267314753894
%N 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.
%C A317806 k = 7, 8, 15, 16, 23, ... A047521(n+1) for n = 1, 2, 3, 4, 5, ... .
%H A317806 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A317806 a(n) = A275714(A047521(n+1),4).
%e A317806 a(1) = 1: 16|25|34|7 with k = 7.
%e A317806 a(2) = 1: 18|27|36|45 with k = 8.
%p A317806 b:= proc() option remember; local i, j, t; `if`(args[1]=0,
%p A317806       `if`(nargs=2, 1, b(args[t] $t=2..nargs)), add(
%p A317806       `if`(args[j] -args[nargs]<0, 0, b(sort([seq(args[i]-
%p A317806       `if`(i=j, args[nargs], 0), i=1..nargs-1)])[],
%p A317806                 args[nargs]-1)), j=1..nargs-1))
%p A317806     end:
%p A317806 a:= proc(n) option remember; (k-> (m->
%p A317806       b((m/4)$4, k)/24)(k*(k+1)/2))(4*n+3/2*(1-(-1)^n))
%p A317806     end:
%p A317806 seq(a(n), n=1..8);
%Y A317806 Cf. A047521, A275714.
%K A317806 nonn
%O A317806 1,3
%A A317806 _Alois P. Heinz_, Aug 07 2018