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%I #19 Feb 08 2023 09:07:50
%S 1,2,6,24,108,544,3264,23040,176832,1563392,15536160,171172224,
%T 2066033472,27146652480,385447394880,5878028516736,95776238793504,
%U 1660164417866304,30496085473606944,591661117634375040,12087628978334638752
%N Number of permutations p of 1,2,...,n satisfying |p(i+4)-p(i)|<>4 for all 1<=i<=n-4.
%C a(n) is also number of ways to place n nonattacking pieces rook + leaper[4,4] on an n X n chessboard.
%H Vaclav Kotesovec, <a href="/A189255/b189255.txt">Table of n, a(n) for n = 1..27</a>
%H 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 Vaclav Kotesovec, <a href="/A189255/a189255.txt">Mathematica program for this sequence</a>
%H 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 Asymptotic (R. Tauraso 2006, quadratic term V. Kotesovec 2011): a(n)/n! ~ (1 + 12/n + 64/n^2)/e^2.
%Y Cf. A002464, A110128, A117574.
%Y Column k=4 of A333706.
%K nonn,hard
%O 1,2
%A _Vaclav Kotesovec_, Apr 19 2011
%E Terms a(26)-a(27) from _Vaclav Kotesovec_, Apr 20 2012
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