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%I #27 Dec 07 2016 23:31:43
%S 1,1,13,133,3631,172082,16566199,3057290265,1105411581741,
%T 776531523355217,1063228770141145384,2834013489992345694498,
%U 14712337761578682394367473,148727865257442275211424889367
%N Number of n X n binary arrays with top left value 1 and no two ones adjacent horizontally, vertically or nw-se diagonally.
%C Main diagonal of A228285.
%H R. H. Hardin, <a href="/A228277/b228277.txt">Table of n, a(n) for n = 1..25</a>
%F No known recurrence.
%e The thirteen solutions for n=3 correspond to the thirteen possible values of 5-bit numbers with no two adjacent bits equal to 1, namely, the matrices
%e ( 1 0 a )
%e ( 0 0 b )
%e ( e d c ) ; with abcde = A014417(0,...,12) = 0, 1, 10, 100, 101, 1000, 1001, 1010, 10000, 10001, 10010, 10100, 10101 (leading zeros omitted). - _M. F. Hasler_, Apr 27 2014
%e Some solutions for n=4:
%e .1..0..0..1. .1..0..0..0. .1..0..0..0. .1..0..0..0. .1..0..0..0
%e .0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..1..0. .0..0..0..0
%e .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..1
%e .1..0..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..0. .0..0..1..0
%e The last example shows that sw-ne (= anti)diagonally adjacent "1"s are allowed. See A228476, A228506 and A228390 for other variants.
%Y Cf. A228277-A228285.
%Y See also the variants A228390, A228476, A228506, etc.
%K nonn
%O 1,3
%A _R. H. Hardin_, Aug 19 2013
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