cp's OEIS Frontend

A318684 Number of ways to split a strict integer partition of n into consecutive subsequences with strictly decreasing sums.

%I A318684 #14 Sep 29 2018 12:57:30
%S A318684 1,1,1,3,3,5,8,11,14,20,28,35,48,61,79,105,129,162,208,257,318,404,
%T A318684 489,600,732,896,1075,1315,1576,1895,2272,2715,3217,3851,4537,5377,
%U A318684 6353,7484,8765,10314,12044,14079,16420,19114,22184,25818,29840,34528,39903,46030
%N A318684 Number of ways to split a strict integer partition of n into consecutive subsequences with strictly decreasing sums.
%e A318684 The a(9) = 20 split partitions:
%e A318684     (9)
%e A318684    (81)   (8)(1)
%e A318684    (72)   (7)(2)
%e A318684    (63)   (6)(3)
%e A318684    (54)   (5)(4)
%e A318684   (432)  (43)(2)  (4)(3)(2)
%e A318684   (621)  (62)(1)  (6)(2)(1)  (6)(21)
%e A318684   (531)  (53)(1)  (5)(3)(1)  (5)(31)
%t A318684 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 A318684 Table[Sum[Length[Select[comps[y],OrderedQ[Total/@#,Greater]&]],{y,Select[IntegerPartitions[n],UnsameQ@@#&]}],{n,30}]
%Y A318684 Cf. A001970, A063834, A316245, A317508, A317546, A317715, A318434, A318683, A319794.
%K A318684 nonn
%O A318684 0,4
%A A318684 _Gus Wiseman_, Sep 29 2018