cp's OEIS Frontend

A317715 Number of ways to split an integer partition of n into consecutive subsequences with equal sums.

%I A317715 #83 Oct 02 2018 10:33:20
%S A317715 1,1,3,4,9,8,21,16,39,38,64,57,146,102,186,211,352,298,593,491,906,
%T A317715 880,1273,1256,2444,1998,3038,3277,4861,4566,7710,6843,10841,10742,
%U A317715 14966,15071,24499,21638,31334,32706,47157,44584,67464,63262,91351,94247,125248
%N A317715 Number of ways to split an integer partition of n into consecutive subsequences with equal sums.
%H A317715 Hiroaki Yamanouchi, <a href="/A317715/b317715.txt">Table of n, a(n) for n = 0..500</a>
%H A317715 Gus Wiseman, <a href="/A317715/a317715.png">The a(8) = 39 constant-sum split partitions.</a>
%H A317715 Gus Wiseman, <a href="/A317715/a317715_1.png">The a(10) = 64 constant-sum split partitions.</a>
%H A317715 Gus Wiseman, <a href="/A317715/a317715_2.png">The a(12) = 146 constant-sum split partitions.</a>
%e A317715 The a(4) = 9 constant-sum split partitions:
%e A317715   (4),
%e A317715   (31),
%e A317715   (22), (2)(2),
%e A317715   (211), (2)(11),
%e A317715   (1111), (11)(11), (1)(1)(1)(1).
%e A317715 The a(6) = 21 constant-sum split partitions:
%e A317715   (6),
%e A317715   (51),
%e A317715   (42),
%e A317715   (411),
%e A317715   (33), (3)(3),
%e A317715   (321), (3)(21),
%e A317715   (3111), (3)(111),
%e A317715   (222), (2)(2)(2),
%e A317715   (2211), (2)(2)(11),
%e A317715   (21111), (21)(111), (2)(11)(11),
%e A317715   (111111), (111)(111), (11)(11)(11), (1)(1)(1)(1)(1)(1).
%t A317715 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 A317715 Table[Sum[Length[Select[comps[y],SameQ@@Total/@#&]],{y,IntegerPartitions[n]}],{n,10}]
%Y A317715 Cf. A000041, A001970, A063834, A316223, A317545, A317546, A319001.
%Y A317715 Cf. A316245, A317508, A318434, A318683, A318684, A319794.
%K A317715 nonn
%O A317715 0,3
%A A317715 _Gus Wiseman_, Sep 29 2018
%E A317715 a(16)-a(46) from _Hiroaki Yamanouchi_, Oct 02 2018