A180682 a(n) is the largest path count within the (right-aligned Ferrers plots of the) partitions of n.

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

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