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A189271 Number of permutations p of 1,2,...,n satisfying |p(i+6)-p(i)|<>6 for all 1<=i<=n-6.

%I A189271 #19 Feb 08 2023 09:08:45
%S A189271 1,2,6,24,120,720,4800,34752,280512,2528256,25282560,278323200,
%T A189271 3289036800,42336448512,589351062528,8820501301248,141215147788800,
%U A189271 2407845089203200,43543159894318080,832618225074748416,16782891792284791296
%N A189271 Number of permutations p of 1,2,...,n satisfying |p(i+6)-p(i)|<>6 for all 1<=i<=n-6.
%C A189271 a(n) is also number of ways to place n nonattacking pieces rook + leaper[6,6] on an n X n chessboard.
%H A189271 Vaclav Kotesovec, <a href="/A189271/b189271.txt">Table of n, a(n) for n = 1..24</a>
%H A189271 Vaclav Kotesovec, <a href="http://www.kotesovec.cz/books/kotesovec_non_attacking_chess_pieces_2013_6ed.pdf">Non-attacking chess pieces</a>, Sixth edition, p. 633, Feb 02 2013.
%H A189271 Vaclav Kotesovec, <a href="/A189271/a189271.txt">Mathematica program for this sequence</a>
%H A189271 Roberto Tauraso, <a href="http://www.emis.de/journals/INTEGERS/papers/g11/g11.Abstract.html">The Dinner Table Problem: The Rectangular Case</a>, INTEGERS: Electronic Journal of Combinatorial Number Theory, Vol. 6 (2006), #A11.
%F A189271 Asymptotic (R. Tauraso 2006, quadratic term V. Kotesovec 2011): a(n)/n! ~ (1 + 20/n + 168/n^2)/e^2.
%F A189271 Generally (for this sequence is d=6): 1/e^2*(1+4(d-1)/n+2d*(3d-4)/n^2+...).
%Y A189271 Cf. A002464, A110128, A117574, A189255, A189256.
%Y A189271 Column k=6 of A333706.
%K A189271 nonn,hard
%O A189271 1,2
%A A189271 _Vaclav Kotesovec_, Apr 19 2011
%E A189271 Terms a(23)-a(24) from _Vaclav Kotesovec_, Apr 21 2012