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Number of nX4 0..1 arrays with every element unequal to 1, 2, 3, 5 or 8 king-move adjacent elements, with upper left element zero.
1

%I #4 May 31 2018 09:16:55

%S 2,45,107,398,1532,5465,21691,82625,320130,1249914,4849312,18947687,

%T 73917602,288506284,1127216287,4401832436,17197042074,67184504771,

%U 262468813621,1025481497968,4006493089212,15653505735334,61159218053112

%N Number of nX4 0..1 arrays with every element unequal to 1, 2, 3, 5 or 8 king-move adjacent elements, with upper left element zero.

%C Column 4 of A305367.

%H R. H. Hardin, <a href="/A305363/b305363.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +7*a(n-2) +3*a(n-3) -58*a(n-4) -30*a(n-5) -30*a(n-6) +125*a(n-7) +151*a(n-8) +229*a(n-9) +460*a(n-10) +144*a(n-11) +1620*a(n-12) +944*a(n-13) +812*a(n-14) -6334*a(n-15) -17545*a(n-16) -26672*a(n-17) -21565*a(n-18) -19950*a(n-19) -27013*a(n-20) -15737*a(n-21) +106640*a(n-22) +326458*a(n-23) +474674*a(n-24) +456825*a(n-25) +322886*a(n-26) +323882*a(n-27) -48715*a(n-28) -1195501*a(n-29) -1744259*a(n-30) -2465476*a(n-31) -3654469*a(n-32) -3454317*a(n-33) -2767636*a(n-34) +426051*a(n-35) +4421796*a(n-36) +5532097*a(n-37) +6346005*a(n-38) +7552979*a(n-39) +5784347*a(n-40) +3998675*a(n-41) +1029839*a(n-42) -2095952*a(n-43) -2807250*a(n-44) -4239130*a(n-45) -4692718*a(n-46) -2620357*a(n-47) -1388185*a(n-48) -1499441*a(n-49) -347150*a(n-50) +375909*a(n-51) -50350*a(n-52) -126855*a(n-53) +12059*a(n-54) -130328*a(n-55) +2866*a(n-56) +48186*a(n-57) -47816*a(n-58) -154032*a(n-59) -97410*a(n-60) -11426*a(n-61) +9204*a(n-62) +13692*a(n-63) +2300*a(n-64) -2040*a(n-65) -480*a(n-66) for n>68

%e Some solutions for n=5

%e ..0..1..0..1. .0..0..0..0. .0..0..1..1. .0..1..0..0. .0..0..1..0

%e ..1..1..1..1. .1..0..1..0. .1..1..0..0. .0..1..1..0. .0..1..0..1

%e ..1..1..0..1. .1..1..1..1. .1..0..0..0. .0..0..1..0. .1..0..1..1

%e ..1..0..0..0. .0..1..1..0. .0..0..0..1. .1..1..0..0. .0..1..1..1

%e ..0..1..1..1. .1..1..0..0. .1..0..1..1. .1..0..0..1. .0..1..1..0

%Y Cf. A305367.

%K nonn

%O 1,1

%A _R. H. Hardin_, May 31 2018