OFFSET
1,8
COMMENTS
Reverse of last row converges to middle value of odd rows: 1, 1, 3, 6, 13, 23, 46, 78, 143, 240, 414, 673, 1127, 1788, 2885, 4514, 7096,10885, 16784, 25338, 38347, 57147, 85094, 125157, ...
Contribution from Robert G. Wilson v, Sep 25 2010: (Start)
\k..1....2....3....4....5....6....7....8....9...10...11...12...13...14...15...16...17...18
n\
..
.1..1
.2..1....1
.3..1....1....1
.4..1....3....1....1
.5..1....3....3....1....1
.6..1....6....6....3....1....1
.7..1....6....9....6....3....1....1
.8..1...10...14...13....6....3....1....1
.9..1...10...24...18...13....6....3....1....1
10..1...15...31...35...23...13....6....3....1....1
11..1...15...45...51...40...23...13....6....3....1....1
12..1...21...64...85...65...46...23...13....6....3....1....1
13..1...21...82..118..111...71...46...23...13....6....3....1....1
14..1...28..107..181..171..128...78...46...23...13....6....3....1....1
15..1...28..144..244..268..203..135...78...46...23...13....6....3....1....1
16..1...36..175..362..393..334..223..143...78...46...23...13....6....3....1....1
17..1...36..221..470..590..503..372..231..143...78...46...23...13....6....3....1....1
18..1...45..279..654..844..800..582..395..240..143...78...46...23...13....6....3....1....1
... (End)
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..5050.
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]]]]; t[n_, k_] := Plus @@ pathcount /@ IntegerPartitions[n, {k}]; Table[ t[n, k], {n, 13}, {k, n}] // Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Wouter Meeussen, Sep 16 2010
STATUS
approved