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%I #8 Oct 20 2018 15:00:53
%S 69,417,2688,17406,112830,731610,4743680,30758256,199437026,
%T 1293154716,8384845368,54367536934,352520397960,2285750623774,
%U 14820861258700,96098815951376,623107002046964,4040240581140500,26197015761022948
%N Number of (n+1) X (2+1) 0..2 arrays colored with the sets of distinct values in every 2 X 2 subblock, with new values 0..2 introduced row-major order.
%H R. H. Hardin, <a href="/A236158/b236158.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) + 19*a(n-2) + 24*a(n-3) - a(n-4) - 22*a(n-5) - 11*a(n-6) - 2*a(n-7) - 2*a(n-8).
%F Empirical g.f.: x*(69 + 210*x + 126*x^2 - 237*x^3 - 399*x^4 - 171*x^5 - 43*x^6 - 27*x^7) / (1 - 3*x - 19*x^2 - 24*x^3 + x^4 + 22*x^5 + 11*x^6 + 2*x^7 + 2*x^8). - _Colin Barker_, Oct 20 2018
%e Some solutions for n=5:
%e ..0..0..1....0..0..1....0..0..1....0..1..1....0..1..2....0..1..2....0..0..1
%e ..0..1..2....0..2..2....0..0..2....1..1..1....1..2..1....0..0..0....2..1..1
%e ..2..2..2....1..1..2....1..2..2....2..2..0....2..2..0....2..0..0....2..2..0
%e ..0..2..2....0..0..0....1..1..0....2..2..2....2..2..2....1..2..0....2..2..0
%e ..1..2..1....0..0..1....2..0..0....2..1..0....1..2..2....1..1..1....2..1..1
%e ..2..1..0....2..2..2....2..0..0....1..0..1....0..2..0....1..1..2....2..0..0
%Y Column 2 of A236164.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 19 2014
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