cp's OEIS Frontend

A364533 Number of strict integer partitions of n containing the sum of no pair of distinct parts. A variation of sum-free strict partitions.

%I A364533 #7 Aug 03 2023 09:04:30
%S A364533 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 A364533 94,111,119,136,160,174,196,222,252,273,315,341,391,425,477,518,602,
%U A364533 636,719,782,886,944,1073,1140,1302,1380,1553,1651,1888,1995,2224,2370
%N A364533 Number of strict integer partitions of n containing the sum of no pair of distinct parts. A variation of sum-free strict partitions.
%e A364533 The a(1) = 1 through a(12) = 11 partitions (A..C = 10..12):
%e A364533   1   2   3    4    5    6    7     8     9     A     B     C
%e A364533           21   31   32   42   43    53    54    64    65    75
%e A364533                     41   51   52    62    63    73    74    84
%e A364533                               61    71    72    82    83    93
%e A364533                               421   521   81    91    92    A2
%e A364533                                           432   631   A1    B1
%e A364533                                           531   721   542   543
%e A364533                                           621         632   732
%e A364533                                                       641   741
%e A364533                                                       731   831
%e A364533                                                       821   921
%t A364533 Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Intersection[#, Total/@Subsets[#,{2}]] == {}&]],{n,0,30}]
%Y A364533 For subsets of {1..n} we have A085489, complement A088809.
%Y A364533 The non-strict version is A236912, complement A237113, ranked by A364461.
%Y A364533 Allowing re-used parts gives A364346.
%Y A364533 The non-binary version is A364349, non-strict A237667 (complement A237668).
%Y A364533 The linear combination-free version is A364350.
%Y A364533 The complement in strict partitions is A364670, w/ re-used parts A363226.
%Y A364533 A000041 counts integer partitions, strict A000009.
%Y A364533 A008284 counts partitions by length, strict A008289.
%Y A364533 A108917 counts knapsack partitions, strict A275972.
%Y A364533 A151897 counts sum-free subsets, complement A364534.
%Y A364533 A323092 counts double-free partitions, ranks A320340.
%Y A364533 Cf. A007865, A025065, A240861, A325862, A326083, A364272, A364345, A364347.
%K A364533 nonn
%O A364533 0,4
%A A364533 _Gus Wiseman_, Aug 02 2023