|
%I #11 Sep 29 2018 12:57:36
%S 1,1,1,3,3,5,9,11,15,20,31,37,52,64,85,111,141,175,225,279,346,437,
%T 532,654,802,979,1182,1438,1740,2083,2502,2996,3565,4245,5043,5950,
%U 7068,8303,9772,11449,13452,15681,18355,21338,24855,28846,33509,38687,44819,51644
%N Number of ways to split a strict integer partition of n into consecutive subsequences with weakly decreasing sums.
%e The a(6) = 9 split partitions:
%e (6)
%e (51) (5)(1)
%e (42) (4)(2)
%e (321) (32)(1) (3)(21) (3)(2)(1).
%t 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 Table[Sum[Length[Select[comps[y],OrderedQ[Total/@#,GreaterEqual]&]],{y,Select[IntegerPartitions[n],UnsameQ@@#&]}],{n,30}]
%Y Cf. A001970, A063834, A316245, A317508, A317546, A317715, A318434, A318683, A318684.
%K nonn
%O 0,4
%A _Gus Wiseman_, Sep 29 2018
|
