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A290202 Number of solid standard Young tableaux of cylindrical shape lambda X 3, where lambda ranges over all partitions of n. 1
1, 1, 10, 276, 14318, 1214358, 150910592, 25454753376, 5599142988564, 1557618719594808, 532482249378122738, 218108013886160729600, 105215894641522373026220, 59025152558043462549357094, 38095446968224172036448488814, 27985301641485576224718954999962 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..15.

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(l) option remember; local m; m:= nops(l);

      `if`({map(x-> x[], l)[]}minus{0}={}, 1, add(add(`if`(l[i][j]>

      `if`(i=m or nops(l[i+1])<j, 0, l[i+1][j]) and l[i][j]>

      `if`(nops(l[i])=j, 0, l[i][j+1]), b(subsop(i=subsop(

       j=l[i][j]-1, l[i]), l)), 0), j=1..nops(l[i])), i=1..m))

    end:

g:= proc(n, i, l) `if`(n=0 or i=1, b(map(x->[3$x], [l[], 1$n])),

       add(g(n-i*j, i-1, [l[], i$j]), j=0..n/i))

    end:

a:= n-> g(n$2, []):

seq(a(n), n=0..10);

CROSSREFS

Column k=3 of A215204.

Sequence in context: A222998 A221526 A153331 * A203149 A117654 A067427

Adjacent sequences:  A290199 A290200 A290201 * A290203 A290204 A290205

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 23 2017

STATUS

approved

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Last modified September 25 22:18 EDT 2021. Contains 347664 sequences. (Running on oeis4.)