A180684 a(n) equals the sum of path counts in the (right-aligned Ferrers plots of) the partitions of n.

1, 2, 3, 6, 9, 18, 27, 49, 77, 129, 199, 329, 497, 787, 1194, 1838, 2738, 4154, 6108, 9098, 13265, 19432, 28024, 40612, 57961, 82958, 117469, 166390, 233520, 327899, 456534, 635503, 878657, 1213450, 1666138, 2285105, 3117131, 4246399, 5758532

Offset

1,2

Comments

Also equals row sums of A180683.

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..100.

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 = 1, s = 0}, While[k < n + 1, s = s + Plus @@ pathcount /@ IntegerPartitions[n, {k}]; k++ ]; s]; Array[f, 39]

Crossrefs

Cf. A180683

Sequence in context: A261661 A062865 A351018 * A206100 A178940 A018264

Adjacent sequences: A180681 A180682 A180683 * A180685 A180686 A180687

Keyword

nonn

Author

Wouter Meeussen, Sep 16 2010

Extensions

a(37) onwards from Robert G. Wilson v, Sep 25 2010

Status

approved