|
| |
|
|
A007579
|
|
Number of Young tableaux of height <= 6.
(Formerly M1217)
|
|
14
|
|
|
|
1, 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)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
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 letters x in word z. - Alois P. Heinz, May 30 2012
|
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
|
Alois P. Heinz, Table of n, a(n) for n = 0..1000
F. Bergeron, L. Favreau and D. Krob, Conjectures on the enumeration of tableaux of bounded height, Preprint. (Annotated scanned copy)
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.
Alon Regev, Amitai Regev, Doron Zeilberger, Identities in character tables of S_n, arXiv preprint arXiv:1507.03499 [math.CO], 2015.
Index entries for sequences related to Young tableaux.
|
|
|
FORMULA
|
a(n) ~ 3/4 * 6^(n+15/2)/(Pi^(3/2)*n^(15/2)). - Vaclav Kotesovec, Sep 11 2013
|
|
|
MAPLE
|
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=0..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
|
|
|
MATHEMATICA
|
RecurrenceTable[{144 (-3+n) (-2+n) (-1+n) a[-4+n]+144 (-2+n) (-1+n) a[-3+n]-4 (-1+n) (33+58 n+10 n^2) a[-2+n]-4 (84+46 n+5 n^2) a[-1+n]+(5+n) (8+n) (9+n) a[n]==0, a[1]==1, a[2]==2, a[3]==4, a[4]==10}, a, {n, 20}] (* Vaclav Kotesovec, Sep 11 2013 *)
|
|
|
CROSSREFS
|
Column k=6 of A182172. - Alois P. Heinz, May 30 2012
Sequence in context: A294672 A239077 A148099 * A239078 A303930 A007123
Adjacent sequences: A007576 A007577 A007578 * A007580 A007581 A007582
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Simon Plouffe
|
|
|
EXTENSIONS
|
More terms from Alois P. Heinz, Apr 10 2012
|
|
|
STATUS
|
approved
|
| |
|
|
