%I #4 Feb 06 2018 13:35:57
%S 2,13,29,112,504,2528,11252,50720,241309,1120649,5164117,24001749,
%T 111611790,517587900,2401369229,11150079663,51754367711,240183038282,
%U 1114814806501,5174545144732,24016953668166,111472218446769
%N Number of nX4 0..1 arrays with every element equal to 1, 2, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
%C Column 4 of A299314.
%H R. H. Hardin, <a href="/A299310/b299310.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) -9*a(n-2) +24*a(n-3) -47*a(n-4) -33*a(n-5) +67*a(n-6) -44*a(n-7) -1266*a(n-8) +1618*a(n-9) -650*a(n-10) +8875*a(n-11) -21535*a(n-12) +45298*a(n-13) -28362*a(n-14) +8063*a(n-15) -33255*a(n-16) +137036*a(n-17) -475039*a(n-18) +685036*a(n-19) -1381737*a(n-20) +2122260*a(n-21) -2994250*a(n-22) +3090285*a(n-23) -1926929*a(n-24) +3223180*a(n-25) -4173823*a(n-26) +4989813*a(n-27) +3861224*a(n-28) -12392223*a(n-29) +10955676*a(n-30) -4368770*a(n-31) +6543615*a(n-32) -28383782*a(n-33) +21197884*a(n-34) -9458914*a(n-35) -3445614*a(n-36) -34122171*a(n-37) +61493313*a(n-38) -7568366*a(n-39) -21654985*a(n-40) +47622275*a(n-41) -5153772*a(n-42) +1833710*a(n-43) -29408089*a(n-44) +26364129*a(n-45) -23403481*a(n-46) -25753860*a(n-47) -1475594*a(n-48) +28400558*a(n-49) -453526*a(n-50) -4211936*a(n-51) -3649669*a(n-52) -41937*a(n-53) +2293068*a(n-54) +1341106*a(n-55) +369512*a(n-56) -276982*a(n-57) -141152*a(n-58) -41792*a(n-59) -9252*a(n-60) +336*a(n-61) +148*a(n-62) for n>66
%e Some solutions for n=5
%e ..0..1..0..0. .0..1..0..0. .0..1..1..0. .0..1..1..1. .0..1..0..1
%e ..0..1..1..0. .0..0..1..1. .1..0..0..1. .0..0..0..0. .0..0..1..1
%e ..1..1..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..1. .1..1..0..0
%e ..0..0..1..1. .0..0..0..1. .1..1..0..0. .1..0..0..1. .0..1..1..1
%e ..1..1..0..1. .0..1..1..0. .0..0..1..0. .0..1..1..0. .1..0..0..1
%Y Cf. A299314.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 06 2018