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A215087 Number of solid standard Young tableaux of n cells and height <= 2. 2
1, 1, 3, 8, 26, 92, 372, 1566, 7086, 33550, 167504, 873226, 4764614, 26947632, 157926628, 954523378, 5945067490, 38060781922, 250345198424, 1688978186742, 11679437620552, 82652840640478, 598018846154666, 4418072084681592, 33298670603875846, 255782905412464810 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..40

S. B. Ekhad, D. Zeilberger, Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux, arXiv:1202.6229v1 [math.CO], 2012

Wikipedia, Young tableau

MAPLE

b:= proc(n, l) option remember; `if`(n=0, 1,

       b(n-1, [l[], [1]])+ add(`if`(i=1 or nops(l[i])<nops(l[i-1]),

       b(n-1, subsop(i=[l[i][], 1], l)), 0)+ add(`if`(l[i][j]<2 and

       (i=1 or l[i][j]<l[i-1][j]) and (j=1 or l[i][j]<l[i][j-1]),

       b(n-1, subsop(i=subsop(j=l[i][j]+1, l[i]), l)), 0),

       j=1..nops(l[i])), i=1..nops(l)))

    end:

a:= n-> b(n, []):

seq(a(n), n=0..20);

CROSSREFS

Column k=2 of A215086.

Sequence in context: A148820 A148821 A074506 * A148822 A124528 A320344

Adjacent sequences:  A215084 A215085 A215086 * A215088 A215089 A215090

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 02 2012

STATUS

approved

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Last modified August 7 06:24 EDT 2020. Contains 336274 sequences. (Running on oeis4.)