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Number of n X 2 0..2 arrays with every nonzero element less than or equal to at least two horizontal and vertical neighbors.
1

%I #8 Jun 04 2018 09:22:51

%S 1,3,9,22,63,209,686,2228,7365,24619,82433,276500,929936,3133114,

%T 10566260,35661359,120433051,406897030,1375168827,4648638160,

%U 15716950105,53145110566,179719928744,607794550141,2055594816788,6952369432018

%N Number of n X 2 0..2 arrays with every nonzero element less than or equal to at least two horizontal and vertical neighbors.

%C Column 2 of A203460.

%H R. H. Hardin, <a href="/A203454/b203454.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) -12*a(n-2) +19*a(n-3) -32*a(n-4) +15*a(n-5) -13*a(n-6) +13*a(n-7) +10*a(n-8) +7*a(n-9) +5*a(n-10) +a(n-11).

%F Empirical g.f.: x*(1 - 3*x + 3*x^2 - 15*x^3 + 14*x^4 + 5*x^5 + 26*x^6 + 18*x^7 + 12*x^8 + 6*x^9 + x^10) / (1 - 6*x + 12*x^2 - 19*x^3 + 32*x^4 - 15*x^5 + 13*x^6 - 13*x^7 - 10*x^8 - 7*x^9 - 5*x^10 - x^11). - _Colin Barker_, Jun 04 2018

%e Some solutions for n=5:

%e ..0..0....1..1....2..2....1..1....2..2....2..2....1..1....0..0....0..0....1..1

%e ..0..0....1..1....2..2....2..2....2..2....2..2....1..1....0..0....2..2....1..1

%e ..1..1....0..0....0..0....2..2....0..2....2..2....2..2....1..1....2..2....2..2

%e ..2..2....2..2....0..0....0..0....2..2....1..1....2..2....1..1....0..0....2..2

%e ..2..2....2..2....0..0....0..0....2..2....0..0....1..1....0..0....0..0....1..1

%Y Cf. A203460.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 02 2012