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Number of 4Xn binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.
1

%I #4 Feb 17 2016 07:29:56

%S 16,126,849,6009,37987,244397,1506570,9258784,55904997,335264275,

%T 1991983545,11763490813,69051103048,403375829894,2346089237885,

%U 13593697842329,78497992061491,451930855824889,2594820580805818

%N Number of 4Xn binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

%C Row 4 of A268995.

%H R. H. Hardin, <a href="/A268998/b268998.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +39*a(n-2) +14*a(n-3) -482*a(n-4) -1102*a(n-5) -111*a(n-6) +1758*a(n-7) +982*a(n-8) -1114*a(n-9) -743*a(n-10) +394*a(n-11) +206*a(n-12) -90*a(n-13) -17*a(n-14) +10*a(n-15) -a(n-16)

%e Some solutions for n=4

%e ..0..1..0..1. .0..1..0..0. .1..1..0..1. .1..0..0..0. .1..0..0..0

%e ..0..1..0..0. .1..0..0..1. .0..0..0..0. .1..0..1..1. .0..1..0..0

%e ..0..0..0..0. .1..0..0..0. .0..0..0..0. .0..0..0..0. .0..1..0..0

%e ..1..1..0..0. .0..1..0..0. .1..0..0..0. .0..1..0..1. .0..0..0..1

%Y Cf. A268995.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 17 2016