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%I #12 Feb 19 2018 12:36:26
%S 0,0,0,1,2,9,34,124,432,1464,4848,15768,50528,159920,500832,1554304,
%T 4785664,14632704,44465664,134378112,404089344,1209699584,3606669824,
%U 10713166848,31713660928,93585811456,275367776256,808068888576
%N Number of n X 1 0..2 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.
%C Column 1 of A280313.
%H R. H. Hardin, <a href="/A280309/b280309.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) - 6*a(n-2) - 16*a(n-3) + 12*a(n-4) + 24*a(n-5) + 8*a(n-6) for n>10.
%F Empirical g.f.: x^4*(1 - 4*x + 3*x^2 + 8*x^3 - 6*x^4 - 12*x^5 - 4*x^6) / (1 - 2*x - 2*x^2)^3. - _Colin Barker_, Feb 19 2018
%e All solutions for n=6:
%e ..0. .0. .0. .0. .0. .0. .0. .0. .0
%e ..0. .1. .0. .1. .0. .0. .1. .1. .0
%e ..0. .2. .0. .1. .1. .0. .1. .0. .0
%e ..0. .2. .0. .1. .1. .1. .1. .0. .0
%e ..1. .2. .1. .1. .1. .1. .1. .0. .1
%e ..0. .2. .1. .0. .1. .1. .2. .0. .2
%Y Cf. A280313.
%K nonn
%O 1,5
%A _R. H. Hardin_, Dec 31 2016
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