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A215266 Number of solid standard Young tableaux of cylindrical shape lambda X 2, where lambda ranges over all partitions of n. 1
1, 1, 4, 26, 258, 3346, 54108, 1054256, 24161966, 634230122, 18806776982, 622011916184, 22754818956246, 912075762692584, 39755634279964662, 1872279469323840472, 94783193260373606758, 5135585509536795416348, 296656123838796109849526, 18200829821539972354967252 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..19.

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->[2$x], [l[], 1$n])),

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

    end:

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

seq(a(n), n=0..12);

CROSSREFS

Column k=2 of A215204.

Sequence in context: A006056 A215242 A098620 * A002465 A248668 A079473

Adjacent sequences:  A215263 A215264 A215265 * A215267 A215268 A215269

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 07 2012

STATUS

approved

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Last modified April 17 23:03 EDT 2021. Contains 343071 sequences. (Running on oeis4.)