This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A364670 #8 Aug 05 2023 06:24:01
%S A364670 0,0,0,0,0,0,1,0,1,0,3,1,4,3,7,6,10,10,14,16,24,25,34,39,48,59,71,81,
%T A364670 103,120,136,166,194,226,260,312,353,419,473,557,636,742,824,974,1097,
%U A364670 1266,1418,1646,1837,2124,2356,2717,3029,3469,3830,4383,4884,5547
%N A364670 Number of strict integer partitions of n with a part equal to the sum of two distinct others. A variation of sum-full strict partitions.
%e A364670 The a(6) = 1 through a(16) = 10 strict partitions (A = 10):
%e A364670 321 . 431 . 532 5321 642 5431 743 6432 853
%e A364670 541 651 6421 752 6531 862
%e A364670 4321 5421 7321 761 7431 871
%e A364670 6321 5432 7521 6532
%e A364670 6431 9321 6541
%e A364670 6521 54321 7432
%e A364670 8321 7621
%e A364670 8431
%e A364670 A321
%e A364670 64321
%t A364670 Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Intersection[#, Total/@Subsets[#,{2}]]!={}&]],{n,0,30}]
%Y A364670 For subsets of {1..n} we have A088809, complement A085489.
%Y A364670 The non-strict version is A237113, complement A236912.
%Y A364670 The non-binary complement is A237667, ranks A364532.
%Y A364670 Allowing re-used parts gives A363226, non-strict A363225.
%Y A364670 The non-binary version is A364272, non-strict A237668.
%Y A364670 The complement is A364533, non-binary A364349.
%Y A364670 A000041 counts integer partitions, strict A000009.
%Y A364670 A008284 counts partitions by length, strict A008289.
%Y A364670 A108917 counts knapsack partitions, strict A275972, ranks A299702.
%Y A364670 A323092 counts double-free partitions, ranks A320340.
%Y A364670 Cf. A007865, A025065, A093971, A111133, A151897, A240861, A325862, A364346, A364350, A364534.
%K A364670 nonn
%O A364670 0,11
%A A364670 _Gus Wiseman_, Aug 03 2023