%I #12 Jul 19 2023 15:20:25
%S 1,40,494,4892,51068,538672,5654616,59369072,623600944,6549786560,
%T 68792261728,722531010240,7588808329152,79705877679872,
%U 837157507203456,8792735883863808,92350844763980544,969968692011129856
%N Number of nX4 0..1 arrays with every one equal to some NW, E or S neighbor.
%H R. H. Hardin, <a href="/A202902/b202902.txt">Table of n, a(n) for n = 1..210</a>
%H Robert Israel, <a href="/A202902/a202902.pdf">Maple-assisted proof of formula</a>
%F Empirical: a(n) = 16*a(n-1) -76*a(n-2) +272*a(n-3) -1060*a(n-4) +2704*a(n-5) -5184*a(n-6) +9920*a(n-7) -11904*a(n-8) +9472*a(n-9) -7168*a(n-10) +4096*a(n-11) -1024*a(n-12).
%F Empirical formula verified by _Robert Israel_, May 09 2018 (see link).
%e Some solutions for n=5
%e ..1..1..1..0....1..0..1..1....0..0..0..0....1..0..0..0....0..1..1..1
%e ..0..1..1..0....1..0..1..1....0..1..1..0....1..1..1..0....1..1..0..1
%e ..0..1..1..1....1..0..1..0....1..0..1..0....1..1..1..0....0..1..1..1
%e ..1..0..1..1....1..1..1..1....1..0..0..0....0..1..0..0....1..1..0..1
%e ..1..1..0..0....0..1..0..0....1..1..0..0....1..1..1..0....0..1..0..0
%p f:= gfun:-rectoproc({a(n) = 16*a(n-1) -76*a(n-2) +272*a(n-3) -1060*a(n-4) +2704*a(n-5) -5184*a(n-6) +9920*a(n-7) -11904*a(n-8) +9472*a(n-9) -7168*a(n-10) +4096*a(n-11) -1024*a(n-12),seq(a(i)=[1, 40, 494, 4892, 51068, 538672, 5654616, 59369072, 623600944, 6549786560, 68792261728, 722531010240][i],i=1..12)},a(n),remember):
%p map(f, [$1..25]); # _Robert Israel_, May 09 2018
%Y Column 4 of A202906.
%K nonn
%O 1,2
%A _R. H. Hardin_, Dec 25 2011