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[ [1 3 5]

[ [2 4 6].

[ [1 4 7] [1 3 7] [1 4 6] [1 3 6] [1 3 6] [1 3 5]

[ [2 5 8] [2 5 8] [2 5 8] [2 5 8] [2 4 8] [2 6 8]

[ [3 6 9] [4 6 9] [3 7 9] [4 7 9] [5 7 9] [4 7 9].

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proposed

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proposed

b[l_, t_] := b[l, t] = Module[{n = Length[l], s = Total[l]}, If[s == 0, 1, Sum[If[t != i && l[[i]] > If[i == n, 0, l[[i + 1]]], b[ReplacePart[l, i -> l[[i]] - 1], i], 0], {i, 1, n}]]];

a[n_] := b[Table[3, n], 0];

Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 29 2018, from first Maple program *)

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Wikipedia, <a href="httphttps://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>

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Alois P. Heinz, <a href="/A214159/b214159_2.txt">Table of n, a(n) for n = 0..700</a>

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OEIS Server: Installed new b-file as b214159.txt.  Old b-file is now b214159_2.txt.

Alois P. Heinz, <a href="/A214159/b214159_2.txt">Table of n, a(n) for n = 0..225700</a>

# second Maple program:

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