login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A213978 Number of solid standard Young tableaux of shape [[n,n,n],[n]]. 10
1, 3, 91, 5471, 464836, 48767805, 5900575762, 791402291063, 114754560003596, 17688389169462060, 2864042102057254739, 482894371222455465001, 84225614036198359288620, 15119622005825185224290830, 2782232873996840900804273236, 523114052492282720617167786279, 100231256005025286627952024093564, 19528383010645472628217323778258916 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Ekhad-Zeilberger give 121 terms.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..129

Shalosh B. Ekhad and Doron Zeilberger, Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux.

S. B. Ekhad and D. Zeilberger, Number of Solid Standard Young Tableaux of shape [[n,n,n],[n]], (n=1..121)

S. B. Ekhad and D. Zeilberger, Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux, arXiv:1202.6229, 2012

FORMULA

Conjecture: Limit n->infinity a(n)^(1/n) = 256. - Vaclav Kotesovec, Jul 17 2014

MAPLE

b:= proc(x, y, z, u) option remember; `if`({x, y, z, u}={0}, 1,

     `if`(x>y and x>u, b(x-1, y, z, u), 0)+`if`(y>z, b(x, y-1, z, u), 0)+

     `if`(z>0, b(x, y, z-1, u), 0)+`if`(u>0, b(x, y, z, u-1), 0))

    end:

a:= n-> b(n$4):

seq(a(n), n=0..20);  # Alois P. Heinz, Jul 19 2012

MATHEMATICA

b[x_, y_, z_, u_] := b[x, y, z, u] = If[Union[{x, y, z, u}] == {0}, 1, If[x>y && x>u, b[x-1, y, z, u], 0] + If[y>z, b[x, y-1, z, u], 0] + If[z>0, b[x, y, z-1, u], 0] + If[u>0, b[x, y, z, u-1], 0]]; a[n_] := b[n, n, n, n]; Table[a[n], {n, 0, 20}] (* Jean-Fran├žois Alcover, Mar 11 2014, after Alois P. Heinz *)

CROSSREFS

Column k=3 of A214722.

Sequence in context: A041439 A300419 A156754 * A318129 A119121 A213987

Adjacent sequences:  A213975 A213976 A213977 * A213979 A213980 A213981

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jul 07 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 17 15:12 EST 2020. Contains 330958 sequences. (Running on oeis4.)