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 A384905 #7 Jun 22 2025 14:37:46
%S A384905 1,0,1,0,1,0,0,1,1,0,0,2,0,0,0,0,2,1,0,0,0,0,3,0,1,0,0,0,0,3,2,0,0,0,
%T A384905 0,0,0,4,2,0,0,0,0,0,0,0,5,2,1,0,0,0,0,0,0,0,6,3,0,1,0,0,0,0,0,0,0,7,
%U A384905 4,1,0,0,0,0,0,0,0,0
%N A384905 Triangle read by rows where T(n,k) is the number of strict integer partitions of n with k maximal anti-runs (decreasing by more than 1).
%e A384905 The T(10,2) = 3 strict partitions with 2 maximal anti-runs are: (7,2,1), (5,4,1), (5,3,2).
%e A384905 Triangle begins:
%e A384905 1
%e A384905 0 1
%e A384905 0 1 0
%e A384905 0 1 1 0
%e A384905 0 2 0 0 0
%e A384905 0 2 1 0 0 0
%e A384905 0 3 0 1 0 0 0
%e A384905 0 3 2 0 0 0 0 0
%e A384905 0 4 2 0 0 0 0 0 0
%e A384905 0 5 2 1 0 0 0 0 0 0
%e A384905 0 6 3 0 1 0 0 0 0 0 0
%e A384905 0 7 4 1 0 0 0 0 0 0 0 0
%e A384905 0 9 3 3 0 0 0 0 0 0 0 0 0
%t A384905 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&Length[Split[#,#1!=#2+1&]]==k&]],{n,0,10},{k,0,n}]
%Y A384905 Row sums are A000009.
%Y A384905 Column k = 1 is A003114.
%Y A384905 For subsets instead of strict integer partitions see A053538, A119900, A210034.
%Y A384905 For runs instead of anti-runs we have A116674, for subsets A034839.
%Y A384905 This is the strict case of A268193.
%Y A384905 A384175 counts subsets with all distinct lengths of maximal runs, complement A384176.
%Y A384905 A384877 gives lengths of maximal anti-runs in binary indices, firsts A384878.
%Y A384905 Cf. A010027, A384177, A384886, A384889, A384890.
%K A384905 nonn,tabl
%O A384905 0,12
%A A384905 _Gus Wiseman_, Jun 21 2025