cp's OEIS Frontend

A318683 Number of ways to split a strict integer partition of n into consecutive subsequences with equal sums.

%I A318683 #16 Sep 29 2018 12:57:23
%S A318683 1,1,1,2,2,3,5,5,7,8,12,12,18,18,26,27,37,38,53,54,73,76,100,104,136,
%T A318683 142,183,192,244,256,327,340,424,448,558,585,722,760,937,983,1195,
%U A318683 1260,1544,1610,1943,2053,2480,2590,3107,3264,3927,4106,4874,5120,6134,6378
%N A318683 Number of ways to split a strict integer partition of n into consecutive subsequences with equal sums.
%e A318683 The a(12) = 18 constant-sum split partitions:
%e A318683   (12)
%e A318683   (7,5)
%e A318683   (8,4)
%e A318683   (9,3)
%e A318683   (10,2)
%e A318683   (11,1)
%e A318683   (5,4,3)
%e A318683   (6,4,2)
%e A318683   (6,5,1)
%e A318683   (7,3,2)
%e A318683   (7,4,1)
%e A318683   (8,3,1)
%e A318683   (9,2,1)
%e A318683   (6)(4,2)
%e A318683   (6)(5,1)
%e A318683   (5,4,2,1)
%e A318683   (6,3,2,1)
%e A318683   (6)(3,2,1)
%t A318683 comps[q_]:=Table[Table[Take[q,{Total[Take[c,i-1]]+1,Total[Take[c,i]]}],{i,Length[c]}],{c,Join@@Permutations/@IntegerPartitions[Length[q]]}];
%t A318683 Table[Sum[Length[Select[comps[y],SameQ@@Total/@#&]],{y,Select[IntegerPartitions[n],UnsameQ@@#&]}],{n,30}]
%Y A318683 Cf. A001970, A063834, A316245, A317508, A317546, A317715, A318434, A318683, A318684, A319794.
%K A318683 nonn
%O A318683 0,4
%A A318683 _Gus Wiseman_, Sep 29 2018