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 A367215 #11 Nov 14 2023 09:50:32
%S A367215 0,0,1,1,2,2,2,3,3,4,5,7,8,10,12,15,18,21,25,29,34,40,46,53,62,71,82,
%T A367215 95,109,124,143,162,185,210,240,270,308,347,393,443,500,562,634,711,
%U A367215 798,895,1002,1120,1252,1397,1558,1735,1930,2146,2383,2644,2930,3245
%N A367215 Number of strict integer partitions of n whose length (number of parts) is not equal to the sum of any subset.
%C A367215 These partitions have Heinz numbers A367225 /\ A005117.
%H A367215 Chai Wah Wu, <a href="/A367215/b367215.txt">Table of n, a(n) for n = 0..118</a>
%e A367215 The a(2) = 1 through a(11) = 7 strict partitions:
%e A367215 (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
%e A367215 (3,1) (4,1) (5,1) (4,3) (5,3) (5,4) (6,4) (6,5)
%e A367215 (6,1) (7,1) (6,3) (7,3) (7,4)
%e A367215 (8,1) (9,1) (8,3)
%e A367215 (5,4,1) (10,1)
%e A367215 (5,4,2)
%e A367215 (6,4,1)
%e A367215 The a(2) = 1 through a(15) = 15 strict partitions (A..F = 10..15):
%e A367215 2 3 4 5 6 7 8 9 A B C D E F
%e A367215 31 41 51 43 53 54 64 65 75 76 86 87
%e A367215 61 71 63 73 74 84 85 95 96
%e A367215 81 91 83 93 94 A4 A5
%e A367215 541 A1 B1 A3 B3 B4
%e A367215 542 642 C1 D1 C3
%e A367215 641 651 652 752 E1
%e A367215 741 742 761 654
%e A367215 751 842 762
%e A367215 841 851 852
%e A367215 941 861
%e A367215 6521 942
%e A367215 951
%e A367215 A41
%e A367215 7521
%t A367215 Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&FreeQ[Total/@Subsets[#], Length[#]]&]], {n,0,30}]
%Y A367215 The following sequences count and rank integer partitions and finite sets according to whether their length is a subset-sum or linear combination of the parts. The current sequence is starred.
%Y A367215 sum-full sum-free comb-full comb-free
%Y A367215 -------------------------------------------
%Y A367215 partitions: A367212 A367213 A367218 A367219
%Y A367215 strict: A367214 A367215* A367220 A367221
%Y A367215 subsets: A367216 A367217 A367222 A367223
%Y A367215 ranks: A367224 A367225 A367226 A367227
%Y A367215 A000041 counts integer partitions, strict A000009.
%Y A367215 A007865/A085489/A151897 count certain types of sum-free subsets.
%Y A367215 A124506 appears to count combination-free subsets, differences of A326083.
%Y A367215 A188431 counts complete strict partitions, incomplete A365831.
%Y A367215 A237667 counts sum-free partitions, ranks A364531.
%Y A367215 A240861 counts strict partitions with length not a part, complement A240855.
%Y A367215 A275972 counts strict knapsack partitions, non-strict A108917.
%Y A367215 A364349 counts sum-free strict partitions, sum-full A364272.
%Y A367215 Triangles:
%Y A367215 A008289 counts strict partitions by length, non-strict A008284.
%Y A367215 A365661 counts strict partitions with a subset-sum k, non-strict A365543.
%Y A367215 A365663 counts strict partitions without a subset-sum k, non-strict A046663.
%Y A367215 A365832 counts strict partitions by subset-sums, non-strict A365658.
%Y A367215 Cf. A002865, A229816, A238628, A364346, A364350, A365312, A365922, A366320.
%K A367215 nonn
%O A367215 0,5
%A A367215 _Gus Wiseman_, Nov 12 2023