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Number of n X 3 0..1 arrays with every nonzero element less than or equal to at least two horizontal and vertical neighbors.
1

%I #12 Jun 04 2018 04:29:27

%S 1,4,17,58,215,866,3507,14120,56921,229860,928443,3749720,15144167,

%T 61165438,247041429,997775144,4029911351,16276407572,65738788527,

%U 265512410122,1072378133103,4331228325504,17493399301365,70654095337584

%N Number of n X 3 0..1 arrays with every nonzero element less than or equal to at least two horizontal and vertical neighbors.

%C Column 3 of A202979.

%H R. H. Hardin, <a href="/A202974/b202974.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 16*a(n-3) - 14*a(n-4) - 3*a(n-5) + 8*a(n-6) - 9*a(n-7) - 2*a(n-8) + 6*a(n-9) + 2*a(n-10).

%F Empirical g.f.: x*(1 - 2*x + 4*x^2 - 16*x^3 + 4*x^4 + x^5 - 10*x^6 + 4*x^7 + 8*x^8 + 2*x^9) / (1 - 6*x + 11*x^2 - 16*x^3 + 14*x^4 + 3*x^5 - 8*x^6 + 9*x^7 + 2*x^8 - 6*x^9 - 2*x^10). - _Colin Barker_, Jun 03 2018

%e Some solutions for n=5:

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

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

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

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

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

%Y Cf. A202979.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 26 2011