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%I #35 Nov 08 2022 02:18:11
%S 1,1,2,6,22,98,534,3414,25498,217338,2080990,22076030,256888218,
%T 3252308706,44497313158,654139144158,10281397705242,172033123244330,
%U 3052895403376110,57266799403366334,1132124282036449570,23524895818926592242
%N Number of permutations p of 1,2,...,n satisfying p(i+3)-p(i)<>3 for all 1<=i<=n-3.
%C a(n) is also number of ways to place n nonattacking pieces rook + semi-leaper[3,3] on an n X n chessboard.
%H Christoph Koutschan, <a href="/A189282/b189282.txt">Table of n, a(n) for n = 0..48</a> (terms 0..30 from Vaclav Kotesovec, terms 31..36 from Manuel Kauers and Christoph Koutschan, terms 37..48 from George Spahn and Doron Zeilberger)
%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="/A189282/a189282.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: a(n)/n! ~ (1 + 5/n + 6/n^2)/e.
%Y Cf. A000255, A189281, A117574.
%K nonn,hard
%O 0,3
%A _Vaclav Kotesovec_, Apr 19 2011