A207542 Number of solid standard Young tableaux with n cells.
1, 1, 3, 9, 33, 135, 633, 3207, 17589, 102627, 636033, 4161141, 28680717, 207318273, 1567344549, 12345147705, 101013795753, 856212871761, 7501911705747, 67815650852235, 631574151445665, 6051983918989833, 59605200185016639, 602764245172225251, 6252962956009863363
Offset: 0
Links
- Shalosh B. Ekhad, Doron Zeilberger, and Vaclav Kotesovec, Table of n, a(n) for n = 0..37 (terms 0..30 from Shalosh B. Ekhad and Doron Zeilberger)
- S. Balakrishnan, S. Govindarajan, and N. S. Prabhakar, On the asymptotics of higher-dimensional partitions, J. Phys. A45 (2012) 055001, arXiv:1105.6231 [cond-mat.stat-mech], 2011.
- Shalosh B. Ekhad and Doron Zeilberger, Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux.
- Suresh Govindarajan, Almost Topological Sequences
Crossrefs
Rows sums of A214753.
Main diagonal of A215086.
Column k=0 of A215120. - Alois P. Heinz, May 12 2014
Programs
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Mathematica
b[n_, k_, L_] := b[n, k, L] = If[n == 0, 1, b[n - 1, k, Append[L, {1}]] + Sum[If[i == 1 || Length[L[[i]]] < Length[L[[i - 1]]], b[n - 1, k, ReplacePart[L, i -> Append[L[[i]], 1]]], 0] + Sum[If[L[[i, j]] < k && (i == 1 || L[[i, j]] < L[[i - 1, j]]) && (j == 1 || L[[i, j]] < L[[i, j - 1]]), b[n - 1, k, ReplacePart[L, i -> ReplacePart[L[[i]], j -> L[[i, j]] + 1]]], 0], {j, 1, Length[L[[i]]]}], {i, 1, Length[L]}]]; A[n_, k_] := If[k == 0, If[n == 0, 1, 0], b[n, Min[n, k], {}]]; T[n_, k_] := A[n, k] - If[k == 0, 0, A[n, k - 1]]; a[n_] := a[n] = Sum[T[n, k], {k, 0, n}]; Table[Print[n, " ", a[n]]; a[n], {n, 0, 20}] (* Jean-François Alcover, Apr 28 2022, after Alois P. Heinz in A214753 *)
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