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 A326017 #13 Jun 05 2021 17:00:53
%S A326017 1,0,1,0,1,1,0,1,1,1,0,1,1,1,1,0,1,1,2,1,1,0,1,1,1,2,1,1,0,1,1,2,3,2,
%T A326017 1,1,0,1,1,2,1,3,2,1,1,0,1,1,2,2,4,3,2,1,1,0,1,1,2,3,1,4,3,2,1,1,0,1,
%U A326017 1,3,3,4,6,4,3,2,1,1,0,1,1,1,1,3,1,6,4
%N A326017 Triangle read by rows where T(n,k) is the number of knapsack partitions of n with maximum k.
%C A326017 An integer partition is knapsack if every distinct submultiset has a different sum.
%H A326017 Fausto A. C. Cariboni, <a href="/A326017/b326017.txt">Table of n, a(n) for n = 0..10010</a>
%H A326017 Fausto A. C. Cariboni, <a href="/A326017/a326017.txt">Conjectures on columns of T(n,k)</a>, Jun 05 2021.
%e A326017 Triangle begins:
%e A326017 1
%e A326017 0 1
%e A326017 0 1 1
%e A326017 0 1 1 1
%e A326017 0 1 1 1 1
%e A326017 0 1 1 2 1 1
%e A326017 0 1 1 1 2 1 1
%e A326017 0 1 1 2 3 2 1 1
%e A326017 0 1 1 2 1 3 2 1 1
%e A326017 0 1 1 2 2 4 3 2 1 1
%e A326017 0 1 1 2 3 1 4 3 2 1 1
%e A326017 0 1 1 3 3 4 6 4 3 2 1 1
%e A326017 0 1 1 1 1 3 1 6 4 3 2 1 1
%e A326017 0 1 1 3 3 5 4 7 6 4 3 2 1 1
%e A326017 0 1 1 2 3 5 4 1 7 6 4 3 2 1 1
%e A326017 0 1 1 2 3 4 6 6 11 7 6 4 3 2 1 1
%e A326017 Row n = 9 counts the following partitions:
%e A326017 (111111111) (22221) (333) (432) (54) (63) (72) (81) (9)
%e A326017 (3222) (441) (522) (621) (711)
%e A326017 (531) (6111)
%e A326017 (51111)
%t A326017 ks[n_]:=Select[IntegerPartitions[n],UnsameQ@@Total/@Union[Subsets[#]]&];
%t A326017 Table[Length[Select[ks[n],Length[#]==k==0||Max@@#==k&]],{n,0,15},{k,0,n}]
%Y A326017 Row sums are A108917.
%Y A326017 Column k = 3 is A326034.
%Y A326017 Cf. A002033, A196723, A275972, A276024.
%Y A326017 Cf. A325592, A325857, A325862, A325863, A325864, A325877, A326016, A326018.
%K A326017 nonn,tabl
%O A326017 0,19
%A A326017 _Gus Wiseman_, Jun 03 2019