A189256 - OEIS

%I #19 Feb 08 2023 09:08:19

%S 1,2,6,24,120,672,4128,28992,231936,2088960,20434944,221871360,

%T 2645370624,34344038400,482103767040,7269498483456,117240911729664,

%U 2013265377314688,36665783917283328,705762463906133760,14313891805008665856

%N Number of permutations p of 1,2,...,n satisfying |p(i+5)-p(i)|<>5 for all 1<=i<=n-5.

%C a(n) is also number of ways to place n nonattacking pieces rook + leaper[5,5] on an n X n chessboard.

%H Vaclav Kotesovec, <a href="/A189256/b189256.txt">Table of n, a(n) for n = 1..26</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="/A189256/a189256.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 + 16/n + 110/n^2)/e^2.

%Y Cf. A002464, A110128, A117574, A189255.

%Y Column k=5 of A333706.

%K nonn,hard

%O 1,2

%A _Vaclav Kotesovec_, Apr 19 2011

%E Terms a(25)-a(26) from _Vaclav Kotesovec_, Apr 20 2012