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A213932
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Number of solid standard Young tableaux of shape [[n,n,n],[n,n]].
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6
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1, 5, 707, 268326, 168146839, 143163177336, 149998192424502, 182598353781240533, 249032962712552804432, 371285830572997665257695, 594729699502746726969433566, 1010574132470951359396337494800, 1804193873947216124589237862262262
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OFFSET
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0,2
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COMMENTS
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Also the number of solid standard Young tableaux of shape [[n,n],[n,n],[n]].
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..30
S. B. Ekhad, D. Zeilberger, Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux, arXiv:1202.6229v1 [math.CO], 2012
Wikipedia, Young tableau
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MAPLE
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b:= proc(l) option remember; local m; m:= nops(l);
`if`({map(x-> x[], l)[]}={0}, 1, add(add(`if`(l[i][j]>
`if`(i=m or nops(l[i+1])<j, 0, l[i+1][j]) and l[i][j]>
`if`(nops(l[i])=j, 0, l[i][j+1]), b(subsop(i=subsop(
j=l[i][j]-1, l[i]), l)), 0), j=1..nops(l[i])), i=1..m))
end:
a:= n-> b([[n, n, n], [n, n]]):
seq(a(n), n=0..10);
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MATHEMATICA
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b[l_] := b[l] = With[{ m = Length[l]}, If[Union[Flatten[l]] == {0}, 1, Sum[Sum[If[l[[i, j]] > If[i == m || Length[l[[i+1]]] < j, 0, l[[i+1, j]]] && l[[i, j]] > If[Length[l[[i]]] == j, 0, l[[i, j+1]]], b[ReplacePart[l, i -> ReplacePart[l[[i]], j -> l[[i, j]]-1]]], 0], {j, 1, Length[l[[i]]]}], {i, 1, m}]]]; a[n_] := b[{{n, n, n}, {n, n}}]; Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Dec 18 2013, translated from Maple *)
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CROSSREFS
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Cf. A213978, A214637, A214638.
Sequence in context: A071772 A201005 A255912 * A199089 A345357 A260481
Adjacent sequences: A213929 A213930 A213931 * A213933 A213934 A213935
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Jul 23 2012
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STATUS
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approved
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