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Number of n X 3 0..2 arrays with no column j greater than or equal to than column j-1 in all rows.
1

%I #13 Jul 21 2018 15:52:27

%S 1,181,9019,331489,10669771,320396041,9245913139,260489615329,

%T 7229878904251,198760197641401,5430623746397059,147781972534146769,

%U 4010919223287633931,108669462396348197161,2940820425317878781779

%N Number of n X 3 0..2 arrays with no column j greater than or equal to than column j-1 in all rows.

%C Column 3 of A212943.

%H R. H. Hardin, <a href="/A212938/b212938.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 55*a(n-1) - 936*a(n-2) + 4860*a(n-3).

%F a(n) = 10^n - 2*18^n + 27^n. - _Vaclav Kotesovec_, May 31 2012

%F Empirical g.f.: x*(1 + 126*x) / ((1 - 10*x)*(1 - 18*x)*(1 - 27*x)). - _Colin Barker_, Jul 21 2018

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A212943.

%K nonn

%O 1,2

%A _R. H. Hardin_, May 31 2012