cp's OEIS Frontend

A365922 Number of non-subset-sums of strict integer partitions of n.

%I A365922 #7 Sep 25 2023 12:55:57
%S A365922 0,1,2,4,8,11,18,25,38,51,70,93,122,159,206,263,328,420,514,645,776,
%T A365922 967,1154,1413,1686,2042,2414,2890,3394,4062,4732,5598,6494,7652,8836,
%U A365922 10329,11884,13833,15830,18376,20936,24131,27476,31547,35780,40966,46292,52737
%N A365922 Number of non-subset-sums of strict integer partitions of n.
%C A365922 For an integer partition y of n, we call a positive integer k <= n a non-subset-sum iff there is no submultiset of y summing to k.
%e A365922 The a(6) = 11 ways, showing each strict partition and its non-subset-sums:
%e A365922     (6): 1,2,3,4,5
%e A365922    (51): 2,3,4
%e A365922    (42): 1,3,5
%e A365922   (321):
%t A365922 Table[Total[Length[Complement[Range[n], Total/@Subsets[#]]]& /@ Select[IntegerPartitions[n], UnsameQ@@#&]],{n,30}]
%Y A365922 The complement (positive subset-sums) is A284640, non-strict A276024.
%Y A365922 Weighted row sums of A365545, non-strict A365923.
%Y A365922 Row sums of A365663, non-strict A046663.
%Y A365922 The non-strict version is A365918.
%Y A365922 The zero-full complement (subset-sums) is A365925, non-strict A304792.
%Y A365922 A000041 counts integer partitions, strict A000009.
%Y A365922 A126796 counts complete partitions, ranks A325781, strict A188431.
%Y A365922 A364350 counts combination-free strict partitions, complement A364839.
%Y A365922 A365543 counts partitions with a submultiset summing to k.
%Y A365922 A365661 counts strict partitions w/ a subset summing to k.
%Y A365922 A365924 counts incomplete partitions, ranks A365830, strict A365831.
%Y A365922 Cf. A006827, A325799, A364272, A365658, A365919, A365921.
%K A365922 nonn
%O A365922 1,3
%A A365922 _Gus Wiseman_, Sep 23 2023