A214875 Number of 4 X n nonconsecutive tableaux.

1, 1, 6, 72, 1289, 29889, 831174, 26455564, 934766625, 35896627737, 1475461220832, 64175536953702, 2928055871469177, 139180794974903769, 6854741942660442918, 348244986517582367748, 18183302860592129336633, 972820066413029570529513, 53192593416458179801289034

Offset: 0

Author

Alois P. Heinz, Jul 28 2012

Keywords

• nonn

Comments

A standard Young tableau (SYT) where entries i and i+1 never appear in the same row is called a nonconsecutive tableau.

Examples

			a(2) = 6:
  [1, 5]  [1, 4]  [1, 3]  [1, 4]  [1, 3]  [1, 3]
  [2, 6]  [2, 6]  [2, 6]  [2, 5]  [2, 5]  [2, 4]
  [3, 7]  [3, 7]  [4, 7]  [3, 7]  [4, 7]  [5, 7]
  [4, 8]  [5, 8]  [5, 8]  [6, 8]  [6, 8]  [6, 8].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..534
• T. Y. Chow, H. Eriksson and C. K. Fan, Chess tableaux, Elect. J. Combin., 11 (2) (2005), #A3.
• S. Dulucq and O. Guibert, Stack words, standard tableaux and Baxter permutations, Disc. Math. 157 (1996), 91-106.
• Wikipedia, Young tableau

Crossrefs

Row n=4 of A214021.

Programs

Maple

a:= proc(n) option remember; `if`(n<3, [1,1,6][n+1], ((1620*n^7
       -13770*n^6 +41958*n^5 -48762*n^4 -6642*n^3 +62532*n^2 -48600*n
       +11664)*a(n-3) +(-3260*n^7 +11360*n^6 -4169*n^5 -19015*n^4
       +14521*n^3 +6179*n^2 -7380*n +1764)*a(n-2) +(-80*n +1964*n^3
       -7469*n^4 +3631*n^2 -5236*n^5 +2590*n^6 +1660*n^7 -300)*a(n-1))
       /((2*n+3)*(n+3)*(10*n^2-15*n-1)*(n+2)^3))
    end:
seq(a(n), n=0..25);

Mathematica

a[0] = a[1] = 1; a[2] = 6; a[n_] := a[n] = ((1620n^7 - 13770n^6 + 41958n^5 - 48762n^4 - 6642n^3 + 62532n^2 - 48600n + 11664) a[n-3] + (-3260n^7 + 11360n^6 - 4169n^5 - 19015n^4 + 14521n^3 + 6179n^2 - 7380n + 1764) a[n-2] + (-80n + 1964n^3 - 7469n^4 + 3631n^2 - 5236n^5 + 2590n^6 + 1660n^7 - 300) a[n-1])/((2n + 3)(n + 3)(10n^2 - 15n - 1)(n + 2)^3);
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Jun 01 2018, from Maple *)

Formula

a(n) ~ 3^(4*n+12) / (2^13 * Pi^(3/2) * n^(15/2)). - Vaclav Kotesovec, Jul 16 2014