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Number of 3 X n 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2, 3 or 4 neighboring 1's.
1

%I #6 May 10 2021 00:50:56

%S 1,4,52,206,734,4088,24801,130159,666434,3560105,19245643,102730864,

%T 546125038,2913904858,15571288925,83122383401,443489006259,

%U 2366877041892,12634189755271,67434790018093,359910312437155,1920940558913908

%N Number of 3 X n 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2, 3 or 4 neighboring 1's.

%C Row 3 of A297762.

%H R. H. Hardin, <a href="/A297764/b297764.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) -5*a(n-2) +8*a(n-3) +53*a(n-4) -295*a(n-5) -76*a(n-6) +556*a(n-7) +178*a(n-8) +196*a(n-9) +145*a(n-10) -779*a(n-11) -628*a(n-12) +226*a(n-13) +100*a(n-14) +275*a(n-15) +152*a(n-16) -65*a(n-17) -32*a(n-18) -26*a(n-19) -4*a(n-20).

%e Some solutions for n=7

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

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

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

%Y Cf. A297762.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 05 2018