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 A214159 Number of n X 3 nonconsecutive tableaux. 3
 1, 0, 1, 6, 72, 960, 14257, 228738, 3896062, 69590192, 1291977768, 24767357824, 487787117424, 9830929279248, 202119964701201, 4228355224663002, 89820746194643154, 1934075860467190608, 42153272431384984926, 928785495190695948612, 20666589509182675178064 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A standard Young tableau (SYT) where entries i and i+1 never appear in the same row is called a nonconsecutive tableau. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..700 T. Y. Chow, H. Eriksson and C. K. Fan, Chess tableaux, Elect. J. Combin., 11 (2) (2005), #A3. Wikipedia, Young tableau FORMULA a(n) ~ 3^(3*n+13/2) / (2^12 * Pi * n^4). - Vaclav Kotesovec, Jul 16 2014 EXAMPLE a(2) = 1: [1 3 5] [2 4 6]. a(3) = 6: [1 4 7] [1 3 7] [1 4 6] [1 3 6] [1 3 6] [1 3 5] [2 5 8] [2 5 8] [2 5 8] [2 5 8] [2 4 8] [2 6 8] [3 6 9] [4 6 9] [3 7 9] [4 7 9] [5 7 9] [4 7 9]. MAPLE b:= proc(l, t) option remember; local n, s; n, s:= nops(l), add(i, i=l); `if`(s=0, 1, add(`if`(t<>i and l[i]> `if`(i=n, 0, l[i+1]), b(subsop(i=l[i]-1, l), i), 0), i=1..n)) end: a:= n-> b([3\$n], 0): seq(a(n), n=0..20); # second Maple program: a:= proc(n) option remember; `if`(n<3, [1, 0, 1][n+1], ((22120*n^5 -58226*n^4 +31547*n^3 +42158*n^2 -53589*n +16146)*a(n-1) -(5988 -27068*n +50360*n^2 -62154*n^3 +49630*n^4 -15400*n^5)*a(n-2) -(7560*n^5 -23058*n^4 +24333*n^3 -11976*n^2 +2967*n -306)*a(n-3)) /(6*(n+2)*(140*n^2-357*n+234)*(n+1)^2)) end: seq(a(n), n=0..25); MATHEMATICA b[l_, t_] := b[l, t] = Module[{n = Length[l], s = Total[l]}, If[s == 0, 1, Sum[If[t != i && l[[i]] > If[i == n, 0, l[[i + 1]]], b[ReplacePart[l, i -> l[[i]] - 1], i], 0], {i, 1, n}]]]; a[n_] := b[Table[3, n], 0]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 29 2018, from first Maple program *) CROSSREFS Column k=3 of A214021. Sequence in context: A067419 A113331 A333593 * A370098 A303342 A332705 Adjacent sequences: A214156 A214157 A214158 * A214160 A214161 A214162 KEYWORD nonn AUTHOR Alois P. Heinz, Jul 05 2012 STATUS approved

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Last modified August 2 21:27 EDT 2024. Contains 374875 sequences. (Running on oeis4.)