%I #4 Dec 25 2017 14:14:44

%S 16,216,2258,26278,304059,3498712,40369420,465695460,5371615378,

%T 61963914640,714775246855,8245166941204,95110883664721,

%U 1097137037898414,12655856242014827,145989698290290048,1684041873726216726

%N Number of nX4 0..1 arrays with no 1 adjacent to 4 king-move neighboring 1s.

%C Column 4 of A297102.

%H R. H. Hardin, <a href="/A297098/b297098.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 14*a(n-1) -28*a(n-2) +94*a(n-3) -1350*a(n-4) +2450*a(n-5) -4020*a(n-6) +45803*a(n-7) -68309*a(n-8) +96186*a(n-9) -663583*a(n-10) +765476*a(n-11) -1275618*a(n-12) +5007651*a(n-13) -4740055*a(n-14) +9380729*a(n-15) -21319664*a(n-16) +19123381*a(n-17) -37373261*a(n-18) +53990476*a(n-19) -46176823*a(n-20) +79054376*a(n-21) -76934482*a(n-22) +33015683*a(n-23) -89023578*a(n-24) -12437985*a(n-25) +56797137*a(n-26) +3691991*a(n-27) +237033110*a(n-28) -36003395*a(n-29) +240855798*a(n-30) -136876578*a(n-31) +88258413*a(n-32) -127736735*a(n-33) +63475433*a(n-34) +30989469*a(n-35) +55884403*a(n-36) +45629990*a(n-37) +2885825*a(n-38) +23016419*a(n-39) -11248309*a(n-40) +2972000*a(n-41) -5777500*a(n-42) +990176*a(n-43) -264530*a(n-44) +29738*a(n-45) -7612*a(n-46) +144*a(n-47)

%e Some solutions for n=4

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

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

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

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

%Y Cf. A297102.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 25 2017