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%I #36 Sep 28 2023 04:27:04
%S 1,9,34,961,25531,2722500,464483559,224546142769,215560806324388,
%T 509113406167679889,2590618817013278596997,30737628149641669227004804,
%U 809724336154415150287031740151,48754690373355654118816600200711441
%N Number of binary arrangements without adjacent 1's on n X n torus connected ne-sw nw-se.
%C If n is odd then A067960(n) = A027683(n).
%C a(18) = 2184710661251680812138610069332410066909052859790416601664. (a(17) = ?) - _Vaclav Kotesovec_, Sep 16 2014
%C a(20) = 61548416926224234005237372092957872593295040887178016957765412173582481. - _Vaclav Kotesovec_, May 18 2021
%H Vaclav Kotesovec, <a href="/A067960/b067960.txt">Table of n, a(n) for n = 1..16</a>
%H Vaclav Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, 2013, p. 440.
%e Neighbors for n=4 (dots represent spaces):
%e . \ /\ /\ /\ /
%e . o..o..o..o
%e . / \/ \/ \/ \
%e . \ /\ /\ /\ /
%e . o..o..o..o
%e . / \/ \/ \/ \
%e . \ /\ /\ /\ /
%e . o..o..o..o
%e . / \/ \/ \/ \
%e . \ /\ /\ /\ /
%e . o..o..o..o
%e . / \/ \/ \/ \
%Y 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 n-s nw-se A067959, e-w ne-sw n-s nw-se A067958, n-s A067961, e-w n-s A027683, e-w ne-sw n-s A066866.
%Y Cf. A212271.
%K nonn,hard,nice
%O 1,2
%A _R. H. Hardin_, Feb 02 2002
%E Terms a(12)-a(16) from _Vaclav Kotesovec_, May 18 2012
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