%I #8 Dec 05 2017 04:09:43
%S 1,4,9,16,64,185,528,2109,7336,25548,96284,350352,1275030,4720164,
%T 17327263,63606177,234363052,861828278,3169215181,11663750978,
%U 42906823150,157839351044,580741120133,2136506975344,7860072868753
%N Number of nX4 0..1 arrays with each 1 adjacent to 3 or 4 king-move neighboring 1s.
%C Column 4 of A296115.
%H R. H. Hardin, <a href="/A296111/b296111.txt">Table of n, a(n) for n = 1..210</a>
%H Robert Israel, <a href="/A296111/a296111.pdf">Maple-aided proof of formula</a>
%F Empirical: a(n) = a(n-1) +7*a(n-2) +21*a(n-3) -6*a(n-4) -85*a(n-5) -132*a(n-6) -69*a(n-7) +142*a(n-8) +445*a(n-9) +490*a(n-10) +185*a(n-11) -220*a(n-12) -588*a(n-13) -549*a(n-14) +23*a(n-15) +683*a(n-16) +168*a(n-17) -655*a(n-18) -594*a(n-19) -256*a(n-20) +387*a(n-21) +385*a(n-22) -14*a(n-23) -86*a(n-24) -20*a(n-25) +6*a(n-26) +2*a(n-27).
%F Empirical formula verified by _Robert Israel_, Dec 05 2017 (see link).
%e Some solutions for n=7
%e ..0..0..0..0. .0..0..0..0. .1..1..0..0. .0..0..0..0. .1..1..0..0
%e ..0..1..0..0. .0..0..0..0. .1..1..0..0. .1..1..0..0. .1..1..0..0
%e ..1..1..1..0. .0..1..1..0. .0..0..0..0. .1..1..0..0. .0..0..0..0
%e ..0..1..0..0. .0..1..1..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
%e ..0..0..0..0. .1..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..0
%e ..1..1..0..0. .1..1..0..0. .0..0..1..1. .0..0..0..0. .0..1..1..1
%e ..1..1..0..0. .1..1..0..0. .0..0..1..1. .0..0..0..0. .0..0..1..0
%Y Cf. A296115.
%K nonn
%O 1,2
%A _R. H. Hardin_, Dec 04 2017