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%I #17 Apr 04 2018 15:44:21
%S 36,1300,47700,1752148,64369764,2364812680,86878417604,3191736905988,
%T 117257942776700,4307819083344444,158260539240359944,
%U 5814171346741659592,213600867349885236600,7847262801829583566600,288292525423375500733688
%N Number of n X 3 0..3 arrays with no element equal the average of immediate neighbors vertically above and horizontally left of it.
%C Column 3 of A209047.
%H R. H. Hardin, <a href="/A209042/b209042.txt">Table of n, a(n) for n = 1..210</a>
%H Robert Israel, <a href="/A209042/a209042_1.pdf">Maple-assisted proof of empirical formula</a>
%F Empirical: a(n) = 23*a(n-1) +491*a(n-2) +570*a(n-3) -2219*a(n-4) -7882*a(n-5) -12517*a(n-6) -6376*a(n-7) -1205*a(n-8) -6747*a(n-9) +4080*a(n-10) +7811*a(n-11) -4675*a(n-12) +1790*a(n-13) +2576*a(n-14) -2905*a(n-15) +513*a(n-16) +621*a(n-17) -27*a(n-18) -81*a(n-19).
%F Formula confirmed by _Robert Israel_, Apr 03 2018 (see link).
%e Some solutions for n=4
%e ..0..1..0....0..1..2....2..1..2....2..0..1....1..0..2....1..3..0....1..0..1
%e ..3..3..2....3..3..0....3..0..2....0..2..0....3..2..1....2..1..3....0..1..3
%e ..1..3..1....0..1..1....2..0..0....1..2..2....1..0..3....0..1..0....1..2..1
%e ..2..3..3....3..3..1....1..3..0....3..0..0....3..0..1....1..2..0....0..2..3
%Y Cf. A209047.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 04 2012
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