A067963 - OEIS

%I #21 Aug 22 2016 16:52:56

%S 2,7,77,1152,56549,3837761,806190208,251170142257,223733272186825,

%T 319544298135448960,1210302996752248488817,7876274672755293629849313,

%U 127662922218147601317696761088,3758866349549535184419575245899295

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

%H R. H. Hardin and Vaclav Kotesovec, <a href="/A067963/b067963.txt">Table of n, a(n) for n = 1..30</a>

%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, 2013, p. 69-71.

%e Neighbors for n=4 (dots represent spaces):

%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

%Y Cf. circle A000204, line A000045, arrays: ne-sw nw-se A067965, 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, 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 Diagonal of A228683

%K nonn,nice,hard

%O 1,1

%A _R. H. Hardin_, Feb 02 2002

%E Terms a(15)-a(19) from _Vaclav Kotesovec_, May 01 2012