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Number of n X 1 0..3 arrays with no element equal to the sum mod 4 of its horizontal and vertical neighbors.
1

%I #10 Mar 29 2018 13:33:05

%S 3,12,27,81,252,729,2187,6588,19683,59049,177228,531441,1594323,

%T 4783212,14348907,43046721,129140892,387420489,1162261467,3486786588,

%U 10460353203,31381059609,94143185388,282429536481,847288609443,2541865848012

%N Number of n X 1 0..3 arrays with no element equal to the sum mod 4 of its horizontal and vertical neighbors.

%C Column 1 of A183508.

%H R. H. Hardin, <a href="/A183503/b183503.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 3*a(n-1) + 3*a(n-3) - 9*a(n-4).

%F Empirical g.f.: 3*x*(1 + x)*(1 - 3*x^2) / ((1 - 3*x)*(1 - 3*x^3)). - _Colin Barker_, Mar 29 2018

%e Some solutions for 3 X 1:

%e ..3....3....3....2....0....3....1....1....2....2....0....0....1....0....2....0

%e ..0....1....1....0....2....2....0....3....1....0....3....3....2....1....3....3

%e ..2....0....3....3....0....0....1....0....0....1....1....2....3....0....0....0

%Y Cf. A183508.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 05 2011