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%I #4 Jan 11 2018 08:20:54
%S 0,5,13,59,346,2197,13350,84657,529728,3332184,20964122,131877463,
%T 829756630,5220895754,32849496926,206690481993,1300503303978,
%U 8182815008750,51486600462026,323955743728628,2038342606416797
%N Number of nX4 0..1 arrays with every element equal to 2, 3, 4 or 6 king-move adjacent elements, with upper left element zero.
%C Column 4 of A298070.
%H R. H. Hardin, <a href="/A298066/b298066.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) +21*a(n-2) +20*a(n-3) -79*a(n-4) -297*a(n-5) -515*a(n-6) -65*a(n-7) +3135*a(n-8) +4790*a(n-9) -9467*a(n-10) -19768*a(n-11) +22520*a(n-12) +41611*a(n-13) -9470*a(n-14) +67882*a(n-15) +127389*a(n-16) -110968*a(n-17) -192960*a(n-18) -459542*a(n-19) -972861*a(n-20) -631438*a(n-21) -403464*a(n-22) +82853*a(n-23) +2308341*a(n-24) +3808053*a(n-25) +4299720*a(n-26) +1368128*a(n-27) +242434*a(n-28) +2969861*a(n-29) -4860102*a(n-30) -2751493*a(n-31) +3510365*a(n-32) -5993208*a(n-33) -2885203*a(n-34) -4604290*a(n-35) -5951332*a(n-36) +2187218*a(n-37) +2171423*a(n-38) +121390*a(n-39) -4212722*a(n-40) -7637013*a(n-41) -4237987*a(n-42) +2916291*a(n-43) -211361*a(n-44) -1418957*a(n-45) -2529996*a(n-46) -99823*a(n-47) +1187281*a(n-48) -239005*a(n-49) +159474*a(n-50) -230785*a(n-51) +137096*a(n-52) -3973*a(n-53) -2523*a(n-54) +5307*a(n-55) +3994*a(n-56) -1228*a(n-57) -1142*a(n-58) +815*a(n-59) +87*a(n-60) -12*a(n-61) +12*a(n-62) for n>63
%e Some solutions for n=7
%e ..0..0..0..1. .0..0..1..1. .0..0..1..1. .0..0..1..1. .0..0..0..0
%e ..1..0..1..1. .0..1..0..1. .0..1..0..1. .0..0..0..1. .0..1..0..1
%e ..1..1..0..0. .1..0..1..1. .1..0..1..1. .1..0..0..1. .1..0..1..1
%e ..0..0..1..0. .1..1..1..1. .1..0..0..1. .1..1..1..1. .1..0..1..0
%e ..0..1..1..0. .0..0..0..0. .1..0..0..1. .1..0..0..1. .0..1..0..0
%e ..1..1..0..0. .0..1..1..0. .0..1..1..0. .0..0..0..1. .0..0..1..1
%e ..1..1..1..0. .1..1..0..0. .0..0..0..0. .0..0..1..1. .0..0..0..1
%Y Cf. A298070.
%K nonn
%O 1,2
%A _R. H. Hardin_, Jan 11 2018
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