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%I #13 Mar 02 2018 02:14:07
%S 1,1,1,2,2,3,3,5,6,7,9,10,14,16,19,23,28,32,42,47,56,66,76,90,107,132,
%T 146,174,202,230,268,314,359,429,471,561,645,735,847,979,1094,1247,
%U 1430,1593,1859,2123,2420,2768,3172,3503,4019,4481,5096,5691,6384,7168,8151
%N a(n) is the largest path count within the (right-aligned Ferrers plots of the) partitions of n.
%H Robert G. Wilson v, <a href="/A180682/b180682.txt">Table of n, a(n) for n = 1..87</a>
%e a(13)=14 because the partition of 13 with largest path count is 4432, producing {1,1,1,1}, {1,2,3,4}, {2,5,9}, {5,14} with closing value 14.
%t pathcount[p_] := Block[{ferr = (0*Range[#1] &) /@ p}, Last[Fold[Rest[FoldList[Plus, 0, Drop[#1, Length[#1] - Length[#2]] + #2]] &, 1 + First[ferr], Rest[ferr]]]]; f[n_] := Block[{k = mx = 1}, While[k < n + 1, m = Max[ pathcount /@ IntegerPartitions[n, {k}]]; If[m > mx, mx = m]; k++]; mx]; k = 1; lst = {}; While[k < 58, a = f@ k; Print[{k, a}]; AppendTo[lst, a]; k++ ]; lst
%K nonn
%O 1,4
%A _Wouter Meeussen_, Sep 16 2010
%E a(37) onwards from _Robert G. Wilson v_, Sep 19 2010
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