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Number of 4Xn 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 0 or 2 neighboring 1s.
1

%I #4 Dec 28 2017 11:33:53

%S 16,55,421,2119,13067,73147,427900,2455970,14209144,81938942,

%T 473153507,2730662734,15762970998,90983791633,525180639202,

%U 3031415452562,17497885523808,101000671437234,582993285761072,3365135765337224

%N Number of 4Xn 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 0 or 2 neighboring 1s.

%C Row 4 of A297338.

%H R. H. Hardin, <a href="/A297341/b297341.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) +14*a(n-2) -11*a(n-3) -57*a(n-4) -53*a(n-5) +129*a(n-6) +56*a(n-7) -129*a(n-8) -104*a(n-9) +534*a(n-10) -425*a(n-11) -247*a(n-12) -410*a(n-13) +1665*a(n-14) -706*a(n-15) -1030*a(n-16) +1934*a(n-17) -1184*a(n-18) -536*a(n-19) +768*a(n-20) -365*a(n-21) +84*a(n-22) +110*a(n-23) -51*a(n-24) +60*a(n-25) -18*a(n-26) -29*a(n-27) -4*a(n-28) -a(n-29) +2*a(n-30) +a(n-31)

%e Some solutions for n=5

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

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

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

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

%Y Cf. A297338.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 28 2017