A117574 - OEIS

%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