cp's OEIS Frontend

A214460 Number of 4 X 2*n+1 nonconsecutive chess tableaux.

%I A214460 #27 Oct 05 2018 20:08:06
%S A214460 1,1,1,1,2,9,44,233,1472,10610,82828,688511,6042580,55523953,
%T A214460 530498426,5242548633,53361716373,557495995958,5961086843092,
%U A214460 65077096683358,723862991146939,8189257485453446,94087399914391254,1096331953010025684,12941148147430923798
%N A214460 Number of 4 X 2*n+1 nonconsecutive chess tableaux.
%C A214460 A standard Young tableau (SYT) with cell(i,j)+i+j == 1 mod 2 for all cells where entries m and m+1 never appear in the same row is called a nonconsecutive chess tableau.
%H A214460 Vaclav Kotesovec, <a href="/A214460/b214460.txt">Table of n, a(n) for n = 0..200</a> (terms 0..70 from Alois P. Heinz)
%H A214460 T. Y. Chow, H. Eriksson and C. K. Fan, <a href="http://www.combinatorics.org/Volume_11/Abstracts/v11i2a3.html">Chess tableaux</a>, Elect. J. Combin., 11 (2) (2005), #A3.
%H A214460 Jonas Sjöstrand, <a href="https://arxiv.org/abs/math/0309231v3">On the sign-imbalance of partition shapes</a>, arXiv:math/0309231v3 [math.CO], 2005.
%H A214460 Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
%F A214460 a(n) ~ c * 16^n / n^(15/2), where c = 5.347555... - _Vaclav Kotesovec_, Dec 05 2017
%e A214460 a(4) = 2:
%e A214460   [1, 4,  7, 12, 15, 20, 23, 28, 31]  [1,   4,  7, 10, 13, 16, 19, 22, 25]
%e A214460   [2, 5, 10, 13, 18, 21, 26, 29, 34]  [2,   5,  8, 11, 14, 17, 28, 31, 34]
%e A214460   [3, 8, 11, 16, 19, 24, 27, 32, 35]  [3,   6,  9, 20, 23, 26, 29, 32, 35]
%e A214460   [6, 9, 14, 17, 22, 25, 30, 33, 36]  [12, 15, 18, 21, 24, 27, 30, 33, 36].
%p A214460 b:= proc(l, t) option remember; local n, s;
%p A214460        n, s:= nops(l), add(i, i=l);
%p A214460       `if`(s=0, 1, add(`if`(t<>i and irem(s+i-l[i], 2)=1 and l[i]>
%p A214460       `if`(i=n, 0, l[i+1]), b(subsop(i=l[i]-1, l), i), 0), i=1..n))
%p A214460     end:
%p A214460 a:= n-> b([(2*n+1)$4], 0):
%p A214460 seq(a(n), n=0..25);
%t A214460 b[l_List, t_] := b[l, t] = Module[{n, s}, {n, s} = {Length[l], Total[l]}; If[s == 0, 1, Sum[If[t != i && Mod[s + i - l[[i]], 2] == 1 && l[[i]] > If[i == n, 0, l[[i+1]]], b[ReplacePart[l, i -> l[[i]]-1], i], 0], {i, 1, n}]]]; a[n_] := b[{2n+1, 2n+1, 2n+1, 2n+1}, 0]; Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Jul 15 2017, translated from Maple *)
%Y A214460 Bisection (odd part) of row n=4 of A214088.
%K A214460 nonn
%O A214460 0,5
%A A214460 _Alois P. Heinz_, Jul 18 2012