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 A290274 Number of solid standard Young tableaux of cylindrical shape lambda X 5, where lambda ranges over all partitions of n. 1
 1, 1, 84, 58604, 118316062, 620383261034, 7137345113624878, 136938419662960675110, 4248619239382421064760418, 208764720295510001353706916224, 15549729565895424021059338656785142, 1588531886834159978895386134546068562294, 215569983507625108792605406075783194767331496 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..12. S. B. Ekhad and D. Zeilberger, Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux, arXiv:1202.6229 [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]) `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->[5\$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..8); MATHEMATICA b[l_] := b[l] = With[{m = Length[l]}, If[Union[l // Flatten] ~Complement~ {0} == {}, 1, Sum[Sum[If[l[[i, j]] > If[i == m || Length[l[[i + 1]]] < j, 0, l[[i + 1, j]]] && l[[i, j]] > If[Length[l[[i]]] == j, 0, l[[i, j + 1]]], b[ReplacePart[l, i -> ReplacePart[l[[i]], j -> l[[i, j]] - 1]]], 0], {j, 1, Length[l[[i]]]}], {i, 1, m}]]]; g[n_, i_, k_, l_] := If[n == 0 || i == 1, b[Table[k, {#}] & /@ Join[l, Table[1, {n}]]], Sum[g[n - i*j, i - 1, k, Join[l, Table[i, {j}]]], {j, 0, n/i}]]; a[n_] := g[n, n, 5, {}]; Table[a[n], {n, 0, 9}] (* Jean-François Alcover, Dec 28 2022, after Alois P. Heinz in A215204 *) CROSSREFS Column k=5 of A215204. Sequence in context: A269897 A184896 A203093 * A289557 A202580 A292196 Adjacent sequences: A290271 A290272 A290273 * A290275 A290276 A290277 KEYWORD nonn AUTHOR Alois P. Heinz, Jul 25 2017 STATUS approved

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Last modified June 8 00:26 EDT 2023. Contains 363157 sequences. (Running on oeis4.)