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%I #11 Dec 01 2017 03:00:29
%S 4,33,120,534,2976,13759,65009,325008,1565481,7539236,36795842,
%T 178342390,863486059,4193371665,20339714386,98614688025,478433693926,
%U 2320695414662,11255335524904,54595627967873,264817091402701,1284455883761926
%N Number of n X 4 0..1 arrays with each 1 adjacent to 1 or 3 king-move neighboring 1's.
%C Column 4 of A295943.
%H R. H. Hardin, <a href="/A295939/b295939.txt">Table of n, a(n) for n = 1..210</a>
%H Robert Israel, <a href="/A295939/a295939.pdf">Maple-assisted proof of formula</a>
%F Empirical: a(n) = 2*a(n-1) + 5*a(n-2) + 52*a(n-3) - 12*a(n-4) - 55*a(n-5) - 505*a(n-6) - 34*a(n-7) - 70*a(n-8) + 1673*a(n-9) + 259*a(n-10) + 938*a(n-11) - 1632*a(n-12) + 663*a(n-13) - 899*a(n-14) + 985*a(n-15) - 542*a(n-16) + 19*a(n-17) + 89*a(n-18) - 104*a(n-19) + 7*a(n-20) - 14*a(n-21).
%F Empirical formula confirmed by _Robert Israel_, Nov 30 2017 (see link).
%e Some solutions for n=7:
%e 0 0 0 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0
%e 0 0 0 1 1 0 0 0 1 0 1 1 0 1 0 1 1 0 0 0
%e 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1
%e 1 1 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0
%e 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 0
%e 1 1 0 0 1 0 0 1 0 1 1 0 0 0 1 0 1 0 1 0
%e 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0
%Y Cf. A295943.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 30 2017
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