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%I #4 Feb 13 2018 11:16:16
%S 2,13,25,78,237,844,2604,8136,26760,86924,277835,899022,2919889,
%T 9444839,30500170,98689584,319463193,1033422691,3342846428,
%U 10816675277,34999690964,113237813316,366379979168,1185473942356,3835735125264
%N Number of nX4 0..1 arrays with every element equal to 1, 2, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.
%C Column 4 of A299574.
%H R. H. Hardin, <a href="/A299570/b299570.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 8*a(n-1) -25*a(n-2) +50*a(n-3) -91*a(n-4) +124*a(n-5) -120*a(n-6) +111*a(n-7) -117*a(n-8) -57*a(n-9) +1422*a(n-10) -2842*a(n-11) +2995*a(n-12) -4038*a(n-13) +6271*a(n-14) -7029*a(n-15) -1871*a(n-16) -15749*a(n-17) +45068*a(n-18) -29238*a(n-19) -11829*a(n-20) -13467*a(n-21) +121211*a(n-22) +105023*a(n-23) -109380*a(n-24) -364968*a(n-25) +909532*a(n-26) -489713*a(n-27) +105583*a(n-28) -1369411*a(n-29) +1850541*a(n-30) -420304*a(n-31) -5805132*a(n-32) +497842*a(n-33) -3558245*a(n-34) +6905661*a(n-35) +1832173*a(n-36) +5566908*a(n-37) +19899549*a(n-38) -9420347*a(n-39) +14803578*a(n-40) -7946936*a(n-41) -11244317*a(n-42) -1408955*a(n-43) -30465026*a(n-44) -6249506*a(n-45) -34375368*a(n-46) +817988*a(n-47) +14972721*a(n-48) +9589036*a(n-49) +20715181*a(n-50) +4441849*a(n-51) +12903307*a(n-52) -5950420*a(n-53) +252652*a(n-54) -4307590*a(n-55) -1421094*a(n-56) -1915678*a(n-57) -919320*a(n-58) +228232*a(n-59) +276920*a(n-60) +280520*a(n-61) -18928*a(n-62) +26896*a(n-63) -3936*a(n-64) -3264*a(n-65) -1152*a(n-66) +256*a(n-67) for n>68
%e Some solutions for n=7
%e ..0..0..1..0. .0..0..1..0. .0..1..0..1. .0..1..0..1. .0..0..1..0
%e ..0..1..1..0. .0..1..1..0. .1..0..0..1. .0..1..1..0. .0..1..1..0
%e ..1..1..1..0. .1..1..1..1. .1..0..0..0. .1..1..1..0. .1..1..1..1
%e ..1..1..1..0. .1..1..1..1. .1..0..0..0. .1..1..1..0. .1..1..1..1
%e ..1..1..1..0. .1..1..1..1. .1..0..0..0. .1..1..1..0. .0..1..1..1
%e ..0..1..1..0. .0..1..1..0. .1..0..1..0. .0..1..1..0. .0..1..0..1
%e ..1..0..0..1. .0..1..0..0. .0..0..1..1. .0..1..0..1. .1..1..0..0
%Y Cf. A299574.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 13 2018
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