login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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.
FORMULA
a(n) ~ 3/4 * 6^(n+15/2)/(Pi^(3/2)*n^(15/2)). - Vaclav Kotesovec, Sep 11 2013
D-finite with recurrence +(n+5)*(n+9)*(n+8)*a(n) +4*(-5*n^2-46*n-84)*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)=0. - R. J. Mathar, Sep 23 2021
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Alois P. Heinz, Apr 10 2012
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 12 23:12 EDT 2024. Contains 374257 sequences. (Running on oeis4.)