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 A325187 #5 Feb 16 2025 08:33:58
%S A325187 1,0,1,3,3,5,9,14,20,26,38,53,75,101,132,175,229,301,394,509,650,826,
%T A325187 1043,1315,1656,2074,2590,3218,3975,4896,6008,7361,8989,10960,13323,
%U A325187 16159,19531,23553,28323,34002,40723,48694,58115,69249,82350,97766,115832
%N A325187 Number of integer partitions of n such that the upper-left square of the Young diagram has strictly greater graph-distance from the lower-right boundary than any other square.
%C A325187 The k-th part of the origin-to-boundary partition of a Young diagram is the number of squares graph-distance k from the lower-right boundary. The sequence gives the number of integer partitions of n whose Young diagram has last part of its origin-to-boundary partition equal to 1.
%C A325187 The Heinz numbers of these partitions are given by A325185.
%H A325187 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphDistance.html">Graph Distance</a>.
%e A325187 The a(1) = 1 through a(8) = 14 partitions:
%e A325187 (1) (21) (22) (41) (51) (61) (71)
%e A325187 (31) (311) (321) (322) (332)
%e A325187 (211) (2111) (411) (331) (422)
%e A325187 (3111) (421) (431)
%e A325187 (21111) (511) (521)
%e A325187 (3211) (611)
%e A325187 (4111) (3221)
%e A325187 (31111) (3311)
%e A325187 (211111) (4211)
%e A325187 (5111)
%e A325187 (32111)
%e A325187 (41111)
%e A325187 (311111)
%e A325187 (2111111)
%t A325187 otb[ptn_]:=Min@@MapIndexed[#1+#2[[1]]-1&,Append[ptn,0]];
%t A325187 Table[Length[Select[IntegerPartitions[n],otb[#]>otb[Rest[#]]&&otb[#]>otb[DeleteCases[#-1,0]]&]],{n,30}]
%Y A325187 Cf. A000245, A188674, A325165, A325169, A325183, A325184, A325185, A325187, A325190, A325191.
%K A325187 nonn
%O A325187 1,4
%A A325187 _Gus Wiseman_, Apr 11 2019