A296830 - OEIS

%I #4 Dec 21 2017 12:42:25

%S 8,31,132,573,2441,10485,44951,192730,826498,3544082,15198081,

%T 65172170,279476178,1198478073,5139392105,22039266498,94511169171,

%U 405291983276,1738017670081,7453162043129,31961457203015,137060728087293

%N Number of nX4 0..1 arrays with each 1 adjacent to 0, 3 or 5 king-move neighboring 1s.

%C Column 4 of A296834.

%H R. H. Hardin, <a href="/A296830/b296830.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) +4*a(n-2) +36*a(n-3) -191*a(n-4) -172*a(n-5) -244*a(n-6) +2863*a(n-7) +2250*a(n-8) -298*a(n-9) -20536*a(n-10) -14014*a(n-11) +8348*a(n-12) +80613*a(n-13) +48318*a(n-14) -35241*a(n-15) -180959*a(n-16) -99366*a(n-17) +73461*a(n-18) +228573*a(n-19) +126168*a(n-20) -72901*a(n-21) -147112*a(n-22) -104887*a(n-23) +8884*a(n-24) +27889*a(n-25) +61467*a(n-26) +45033*a(n-27) +30859*a(n-28) -18608*a(n-29) -33443*a(n-30) -35278*a(n-31) -15633*a(n-32) +3073*a(n-33) +19582*a(n-34) +23473*a(n-35) +7766*a(n-36) -5789*a(n-37) -12917*a(n-38) -5489*a(n-39) +331*a(n-40) +3658*a(n-41) +2145*a(n-42) +389*a(n-43) -593*a(n-44) -675*a(n-45) -214*a(n-46) +38*a(n-47) +148*a(n-48) +72*a(n-49) +24*a(n-50)

%e Some solutions for n=7

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

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

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

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

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

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

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

%Y Cf. A296834.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 21 2017