cp's OEIS Frontend

A067958 Number of binary arrangements without adjacent 1's on n X n torus connected e-w ne-sw n-s nw-se.

%I A067958 #25 Sep 17 2023 21:36:06
%S A067958 1,5,10,133,1411,42938,1796859,157763829,22909432780,6291183426165,
%T A067958 3032485231813445,2674030233698391466,4216437656471537450175,
%U A067958 12038380931111061789962901,61810608197507432888286102310,572863067272579464080483552434421
%N A067958 Number of binary arrangements without adjacent 1's on n X n torus connected e-w ne-sw n-s nw-se.
%C A067958 For n > 1, a(n) is also the number of ways to populate an n X n toroidal chessboard with non-attacking kings (including the case of zero kings). - _Vaclav Kotesovec_, Oct 10 2011
%H A067958 V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, 2013, p. 214.
%e A067958 Neighbors for n=4:
%e A067958   :\|/\|/\|/\|/
%e A067958   :-o--o--o--o-
%e A067958   :/|\/|\/|\/|\
%e A067958   :\|/\|/\|/\|/
%e A067958   :-o--o--o--o-
%e A067958   :/|\/|\/|\/|\
%e A067958   :\|/\|/\|/\|/
%e A067958   :-o--o--o--o-
%e A067958   :/|\/|\/|\/|\
%e A067958   :\|/\|/\|/\|/
%e A067958   :-o--o--o--o-
%e A067958   :/|\/|\/|\/|\
%Y A067958 Cf. circle A000204, line A000045, arrays: ne-sw nw-se A067965, e-w ne-sw nw-se A067963, n-s nw-se A067964, e-w n-s nw-se A066864, e-w ne-sw n-s nw-se A063443, n-s A067966, e-w n-s A006506, nw-se A067962, toruses: bare A002416, ne-sw nw-se A067960, ne-sw n-s nw-se A067959, n-s A067961, e-w n-s A027683, e-w ne-sw n-s A066866.
%Y A067958 Cf. A212269.
%K A067958 nonn,hard
%O A067958 1,2
%A A067958 _R. H. Hardin_, Feb 02 2002
%E A067958 a(14) from _Vaclav Kotesovec_, Aug 22 2016
%E A067958 a(15)-a(16) from _Vaclav Kotesovec_, May 15 2021