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%I #28 Feb 05 2023 10:17:41
%S 1,1,2,6,20,80,384,2240,15424,123456,1110928,11287232,127016304,
%T 1565107248,20935873872,301974271248,4669727780624,77046043259824,
%U 1350585114106416,25062108668100208,490725684463001488,10109820295907492304
%N Total number of permutations p of [n] such that |p(i+3) - p(i)| is not equal to 3 for 1 <= i <= n-3.
%C a(n) is also number of ways to place n nonattacking pieces rook + leaper[3,3] on an n X n chessboard.
%H Vaclav Kotesovec, <a href="/A117574/b117574.txt">Table of n, a(n) for n = 0..30</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="/A117574/a117574.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 Formula given in Tauraso reference.
%F Asymptotic (R. Tauraso 2006, quadratic term V. Kotesovec 2011): a(n)/n! ~ (1 + 8/n + 30/n^2)/e^2.
%Y Cf. A002464, A110128.
%Y Column k=3 of A333706.
%K nonn,hard
%O 0,3
%A _James A. Sellers_, Apr 27 2006
%E Terms a(17)-a(28) from _Vaclav Kotesovec_, Apr 19 2011
%E Terms a(29)-a(30) from _Vaclav Kotesovec_, Apr 20 2012
%E a(0)=1 prepended by _Alois P. Heinz_, Feb 05 2023
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