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%I #7 Aug 03 2023 09:04:30
%S 1,1,1,2,2,3,3,5,5,8,7,11,11,15,15,21,22,28,32,38,40,51,55,65,74,83,
%T 94,111,119,136,160,174,196,222,252,273,315,341,391,425,477,518,602,
%U 636,719,782,886,944,1073,1140,1302,1380,1553,1651,1888,1995,2224,2370
%N Number of strict integer partitions of n containing the sum of no pair of distinct parts. A variation of sum-free strict partitions.
%e The a(1) = 1 through a(12) = 11 partitions (A..C = 10..12):
%e 1 2 3 4 5 6 7 8 9 A B C
%e 21 31 32 42 43 53 54 64 65 75
%e 41 51 52 62 63 73 74 84
%e 61 71 72 82 83 93
%e 421 521 81 91 92 A2
%e 432 631 A1 B1
%e 531 721 542 543
%e 621 632 732
%e 641 741
%e 731 831
%e 821 921
%t Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Intersection[#, Total/@Subsets[#,{2}]] == {}&]],{n,0,30}]
%Y For subsets of {1..n} we have A085489, complement A088809.
%Y The non-strict version is A236912, complement A237113, ranked by A364461.
%Y Allowing re-used parts gives A364346.
%Y The non-binary version is A364349, non-strict A237667 (complement A237668).
%Y The linear combination-free version is A364350.
%Y The complement in strict partitions is A364670, w/ re-used parts A363226.
%Y A000041 counts integer partitions, strict A000009.
%Y A008284 counts partitions by length, strict A008289.
%Y A108917 counts knapsack partitions, strict A275972.
%Y A151897 counts sum-free subsets, complement A364534.
%Y A323092 counts double-free partitions, ranks A320340.
%Y Cf. A007865, A025065, A240861, A325862, A326083, A364272, A364345, A364347.
%K nonn
%O 0,4
%A _Gus Wiseman_, Aug 02 2023