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%I #4 Jun 07 2018 08:59:06
%S 8,28,78,334,1516,6329,27110,118085,519355,2275485,10007094,44192714,
%T 194914769,860631159,3804114731,16808740747,74300020431,328513615351,
%U 1452355332413,6421729825720,28395939285931,125559090180746
%N Number of nX4 0..1 arrays with every element unequal to 0, 1, 2, 4, 5 or 6 king-move adjacent elements, with upper left element zero.
%C Column 4 of A305642.
%H R. H. Hardin, <a href="/A305638/b305638.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 5*a(n-1) +a(n-2) +36*a(n-3) -249*a(n-4) -61*a(n-5) -301*a(n-6) +4148*a(n-7) +3004*a(n-8) -1897*a(n-9) -32304*a(n-10) -46560*a(n-11) +27683*a(n-12) +137258*a(n-13) +281069*a(n-14) -57027*a(n-15) -342232*a(n-16) -506107*a(n-17) -37426*a(n-18) +554229*a(n-19) -1071467*a(n-20) -898278*a(n-21) +113368*a(n-22) +3803483*a(n-23) +472051*a(n-24) -4424283*a(n-25) +1559246*a(n-26) +3356876*a(n-27) +3532614*a(n-28) -3042945*a(n-29) +6636551*a(n-30) +17850022*a(n-31) +8400099*a(n-32) -11687308*a(n-33) -24486823*a(n-34) -2662032*a(n-35) -24508906*a(n-36) -44534827*a(n-37) -34883725*a(n-38) -8259004*a(n-39) +30416901*a(n-40) +13943043*a(n-41) +32010563*a(n-42) +30849876*a(n-43) +15374803*a(n-44) +40574097*a(n-45) +36979452*a(n-46) +13755094*a(n-47) -15128558*a(n-48) -12893233*a(n-49) -1964205*a(n-50) -2251916*a(n-51) +200153*a(n-52) +283036*a(n-53) +778936*a(n-54) -353165*a(n-55) -1367887*a(n-56) +200589*a(n-57) +542316*a(n-58) +68855*a(n-59) -157236*a(n-60) -100632*a(n-61) +8908*a(n-62) +16806*a(n-63) +1668*a(n-64) -240*a(n-65) for n>67
%e Some solutions for n=5
%e ..0..1..0..0. .0..1..0..0. .0..0..0..0. .0..1..0..0. .0..0..0..0
%e ..1..0..0..0. .1..0..0..0. .0..1..1..0. .0..0..1..0. .0..0..0..1
%e ..0..0..0..0. .0..0..0..0. .1..0..1..0. .0..1..1..0. .0..1..0..0
%e ..0..0..1..1. .0..0..1..1. .0..0..1..1. .1..0..0..0. .0..1..1..0
%e ..0..0..1..1. .1..1..1..1. .0..0..1..1. .1..1..1..0. .1..1..0..1
%Y Cf. A305642.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jun 07 2018
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