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%I #6 Apr 23 2021 14:29:05
%S 0,5,6,27,57,87,161,361,898,1984,4089,8938,20136,45253,100907,226408,
%T 508923,1143285,2565894,5762902,12955110,29139440,65553446,147496388,
%U 331934544,747140540,1681925878,3786696312,8526308067,19200092288
%N Number of n X 6 0..1 arrays with every element equal to 2, 3, 6 or 8 king-move adjacent elements, with upper left element zero.
%C Column 6 of A298177.
%H R. H. Hardin, <a href="/A298175/b298175.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) +4*a(n-2) -7*a(n-3) +6*a(n-4) -6*a(n-5) -45*a(n-6) +29*a(n-7) +a(n-8) -8*a(n-9) +168*a(n-10) +22*a(n-11) +70*a(n-12) +224*a(n-13) -187*a(n-14) -232*a(n-15) -533*a(n-16) -1351*a(n-17) -1185*a(n-18) -705*a(n-19) +302*a(n-20) +2705*a(n-21) +4721*a(n-22) +5745*a(n-23) +5399*a(n-24) +2008*a(n-25) -3457*a(n-26) -9611*a(n-27) -14924*a(n-28) -15983*a(n-29) -11662*a(n-30) -2510*a(n-31) +9674*a(n-32) +20329*a(n-33) +25192*a(n-34) +22515*a(n-35) +13198*a(n-36) +166*a(n-37) -12413*a(n-38) -20590*a(n-39) -22316*a(n-40) -17694*a(n-41) -8975*a(n-42) +431*a(n-43) +7972*a(n-44) +11703*a(n-45) +11072*a(n-46) +7575*a(n-47) +3130*a(n-48) -633*a(n-49) -2741*a(n-50) -3230*a(n-51) -2632*a(n-52) -1527*a(n-53) -545*a(n-54) +57*a(n-55) +394*a(n-56) +451*a(n-57) +326*a(n-58) +184*a(n-59) +36*a(n-60) -30*a(n-61) -43*a(n-62) -30*a(n-63) -8*a(n-64) +2*a(n-66) +a(n-67) for n > 74.
%e Some solutions for n=7
%e ..0..0..1..0..1..1. .0..0..0..0..0..0. .0..0..1..1..1..0. .0..0..0..0..1..1
%e ..0..1..0..1..0..1. .0..1..1..1..1..0. .1..0..0..1..0..0. .0..1..1..1..0..1
%e ..1..1..0..1..0..0. .1..0..0..0..0..1. .1..1..1..1..1..0. .1..0..0..0..0..1
%e ..0..1..0..1..0..1. .0..1..1..1..1..0. .0..0..0..0..0..1. .0..1..1..1..1..0
%e ..0..0..0..1..1..1. .1..0..0..0..0..1. .0..1..1..1..1..0. .1..0..0..0..0..1
%e ..0..1..0..1..0..1. .0..1..1..1..0..1. .0..1..0..0..0..1. .1..0..1..1..1..0
%e ..1..1..1..0..0..0. .0..0..0..0..1..1. .0..0..1..1..1..1. .1..1..0..0..0..0
%Y Cf. A298177.
%K nonn
%O 1,2
%A _R. H. Hardin_, Jan 14 2018
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