A189284 - OEIS

%I #27 Nov 08 2022 02:18:05

%S 1,1,2,6,24,120,696,4572,34260,290328,2751480,28686024,328764732,

%T 4106158164,55495145304,806797105320,12554890849992,208164423163908,

%U 3663256621120548,68188490015132040,1338490745511631080,27630826605742438968

%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 + semi-leaper[5,5] on an n X n chessboard.

%H Vaclav Kotesovec, <a href="/A189284/b189284.txt">Table of n, a(n) for n = 0..26</a> (Updated Jan 19 2019)

%H Vaclav Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, 2013, p. 644.

%H Vaclav Kotesovec, <a href="/A189284/a189284.txt">Mathematica program for this sequence</a>

%H George Spahn and Doron Zeilberger, <a href="https://arxiv.org/abs/2211.02550">Counting Permutations Where The Difference Between Entries Located r Places Apart Can never be s (For any given positive integers r and s)</a>, arXiv:2211.02550 [math.CO], 2022.

%F Asymptotics (V. Kotesovec, Mar 2011): a(n)/n! ~ (1 + 9/n + 20/n^2)/e.

%Y Cf. A000255, A189281, A189282, A189283, A189256.

%K nonn,hard

%O 0,3

%A _Vaclav Kotesovec_, Apr 19 2011

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