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A007579
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Number of Young tableaux of height <= 6.
(Formerly M1217)
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10
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1, 2, 4, 10, 26, 76, 231, 756, 2556, 9096, 33231, 126060, 488488, 1948232, 7907185, 32831370, 138321690, 593610420, 2579109780, 11377862340, 50726936820, 229078351992, 1043999256966, 4810194384348, 22340617618860, 104742353862360, 494547143860035
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Also the number of n-length words w over 6-ary alphabet {a1,a2,...,a6} such that for every prefix z of w we have #(z,a1) >= #(z,a2) >= ... >= #(z,a6), where #(z,x) counts the number of letters x in word z. - Alois P. Heinz, May 30 2012
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REFERENCES
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F. Bergeron, L. Favreau and D. Krob, Conjectures on the enumeration of tableaux of bounded height, Discrete Math, vol. 139, no. 1-3 (1995), 463-468.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..400
Index entries for sequences related to Young tableaux.
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MAPLE
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h:= proc(l) local n; n:=nops(l); add(i, i=l)! /mul (mul (1+l[i]-j
+add (`if`(l[k]>=j, 1, 0), k=i+1..n), j=1..l[i]), i=1..n)
end:
g:= proc(n, i, l) option remember;
`if`(n=0, h(l), `if`(i=1, h([l[], 1$n]), `if`(i<1, 0,
g(n, i-1, l) +`if`(i>n, 0, g(n-i, i, [l[], i])))))
end:
a:= n-> g(n, 6, []):
seq (a(n), n=1..30); # Alois P. Heinz, Apr 18 2012
# second Maple program
a:= proc(n) option remember;
`if`(n<4, [1, 1, 2, 4][n+1], ((20*n^2+184*n+336)*a(n-1)
+4*(n-1)*(10*n^2+58*n+33)*a(n-2) -144*(n-1)*(n-2)*a(n-3)
-144*(n-1)*(n-2)*(n-3)*a(n-4))/ ((n+5)*(n+8)*(n+9)))
end:
seq (a(n), n=0..30); # Alois P. Heinz, Oct 12 2012
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CROSSREFS
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Column k=6 of A182172. - Alois P. Heinz, May 30 2012
Sequence in context: A006251 A049401 A148099 * A007123 A220871 A007578
Adjacent sequences: A007576 A007577 A007578 * A007580 A007581 A007582
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KEYWORD
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nonn
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AUTHOR
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Simon Plouffe
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EXTENSIONS
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More terms from Alois P. Heinz, Apr 10 2012
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STATUS
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approved
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