cp's OEIS Frontend

A364272 Number of strict integer partitions of n containing the sum of some subset of the parts. A variation of sum-full strict partitions.

%I A364272 #8 Aug 03 2023 09:04:15
%S A364272 0,0,0,0,0,0,1,0,1,0,3,1,4,3,8,6,11,10,17,16,26,25,39,39,54,60,82,84,
%T A364272 116,126,160,177,222,242,302,337,402,453,542,601,722,803,936,1057,
%U A364272 1234,1373,1601,1793,2056,2312,2658,2950,3395,3789,4281,4814,5452,6048
%N A364272 Number of strict integer partitions of n containing the sum of some subset of the parts. A variation of sum-full strict partitions.
%C A364272 First differs from A316402 at a(16) = 11 due to (7,5,3,1).
%e A364272 The a(6) = 1 through a(16) = 11 partitions (A=10):
%e A364272   (321) . (431) . (532)  (5321) (642)  (5431) (743)  (6432)  (853)
%e A364272                   (541)         (651)  (6421) (752)  (6531)  (862)
%e A364272                   (4321)        (5421) (7321) (761)  (7431)  (871)
%e A364272                                 (6321)        (5432) (7521)  (6532)
%e A364272                                               (6431) (9321)  (6541)
%e A364272                                               (6521) (54321) (7432)
%e A364272                                               (7421)         (7621)
%e A364272                                               (8321)         (8431)
%e A364272                                                              (8521)
%e A364272                                                              (A321)
%e A364272                                                              (64321)
%t A364272 Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Intersection[#, Total/@Subsets[#,{2,Length[#]}]]!={}&]],{n,0,30}]
%Y A364272 The non-strict complement is A237667, ranks A364531.
%Y A364272 The non-strict version is A237668, ranks A364532.
%Y A364272 The complement in strict partitions is A364349, binary A364533.
%Y A364272 The linear combination-free version is A364350.
%Y A364272 For subsets of {1..n} we have A364534, complement A151897.
%Y A364272 The binary version is A364670, allowing re-used parts A363226.
%Y A364272 A000041 counts integer partitions, strict A000009.
%Y A364272 A008284 counts partitions by length, strict A008289.
%Y A364272 A108917 counts knapsack partitions, strict A275972, ranks A299702.
%Y A364272 A236912 counts binary sum-free partitions, complement A237113.
%Y A364272 A323092 counts double-free partitions, ranks A320340.
%Y A364272 Cf. A007865, A025065, A085489, A093971, A111133, A240861, A320347, A325862, A363225, A364346.
%K A364272 nonn
%O A364272 0,11
%A A364272 _Gus Wiseman_, Aug 01 2023