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Number of n X 2 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.
1

%I #11 Jun 02 2018 10:35:06

%S 3,35,265,1849,13345,96941,701275,5071167,36689027,265439091,

%T 1920308033,13892446697,100505282121,727107537885,5260271847715,

%U 38055531396239,275313438949691,1991760080088995,14409424470217081,104245243244589977

%N Number of n X 2 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.

%C Column 2 of A202889.

%H R. H. Hardin, <a href="/A202883/b202883.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) +2*a(n-2) +46*a(n-3) +25*a(n-4) +36*a(n-5).

%F Empirical g.f.: (3 + 17*x + 49*x^2 + 51*x^3 + 36*x^4) / (1 - 6*x - 2*x^2 - 46*x^3 - 25*x^4 - 36*x^5). - _Colin Barker_, Jun 02 2018

%e Some solutions for n=5:

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

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

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

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

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

%Y Cf. A202889.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 25 2011