%I #6 Apr 16 2023 20:47:52
%S 0,36,618,6284,73140,766472,7774180,77796496,762302160,7378886108,
%T 70685503542,671138516516,6326727994922,59273960871188,
%U 552390880671856,5124280101956484,47344145084965492,435863812736016840
%N Number of n X 4 0..1 arrays with no 1 equal to more than two of its king-move neighbors, with the exception of exactly one element.
%C Column 4 of A282560.
%H R. H. Hardin, <a href="/A282556/b282556.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 14*a(n-1) -17*a(n-2) -190*a(n-3) -1006*a(n-4) +3164*a(n-5) +7125*a(n-6) +5766*a(n-7) -66778*a(n-8) +34886*a(n-9) +25834*a(n-10) -85288*a(n-11) +31315*a(n-12) -51976*a(n-13) -9686*a(n-14) +30964*a(n-15) -43541*a(n-16) +5466*a(n-17) -6977*a(n-18) +1458*a(n-19) +7732*a(n-20) -372*a(n-21) -343*a(n-22) -394*a(n-23) -104*a(n-24) +50*a(n-25) +4*a(n-27) -a(n-28).
%e Some solutions for n=4
%e ..1..0..0..1. .0..1..0..1. .0..1..0..0. .1..1..0..1. .1..1..0..1
%e ..0..0..0..0. .0..0..1..1. .0..0..0..1. .0..0..1..0. .0..0..1..1
%e ..1..1..0..0. .0..0..0..0. .0..1..0..0. .1..0..0..1. .0..0..0..0
%e ..1..0..1..1. .0..1..0..0. .0..1..1..1. .1..1..0..1. .1..1..0..0
%Y Cf. A282560.
%K nonn
%O 1,2
%A _R. H. Hardin_, Feb 18 2017