A215266 Number of solid standard Young tableaux of cylindrical shape lambda X 2, where lambda ranges over all partitions of n.

1, 1, 4, 26, 258, 3346, 54108, 1054256, 24161966, 634230122, 18806776982, 622011916184, 22754818956246, 912075762692584, 39755634279964662, 1872279469323840472, 94783193260373606758, 5135585509536795416348, 296656123838796109849526, 18200829821539972354967252

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