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 A180682 a(n) is the largest path count within the (right-aligned Ferrers plots of the) partitions of n. 4
 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, 146, 174, 202, 230, 268, 314, 359, 429, 471, 561, 645, 735, 847, 979, 1094, 1247, 1430, 1593, 1859, 2123, 2420, 2768, 3172, 3503, 4019, 4481, 5096, 5691, 6384, 7168, 8151 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Robert G. Wilson v, Table of n, a(n) for n = 1..87 EXAMPLE 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. MATHEMATICA 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 CROSSREFS Sequence in context: A206439 A097450 A062303 * A227426 A229950 A050318 Adjacent sequences:  A180679 A180680 A180681 * A180683 A180684 A180685 KEYWORD nonn AUTHOR Wouter Meeussen, Sep 16 2010 EXTENSIONS a(37) onwards from Robert G. Wilson v, Sep 19 2010 STATUS approved

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Last modified November 16 02:33 EST 2018. Contains 317252 sequences. (Running on oeis4.)