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A199142 Number of n X 1 0..3 arrays with values 0..3 introduced in row major order and each element equal to one or two horizontal and vertical neighbors. 3

%I #8 Feb 22 2018 12:57:30

%S 0,1,1,2,3,6,11,23,47,102,221,492,1099,2485,5637,12858,29391,67354,

%T 154539,355003,816035,1876862,4318201,9937840,22874731,52659593,

%U 121237417,279141170,642732027,1479959118,3407837387,7847200511

%N Number of n X 1 0..3 arrays with values 0..3 introduced in row major order and each element equal to one or two horizontal and vertical neighbors.

%C Column 1 of A199149.

%H R. H. Hardin, <a href="/A199142/b199142.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 3*a(n-1) + a(n-2) - 7*a(n-3) + a(n-4) + 3*a(n-5) for n>6.

%F Empirical g.f.: x^2*(1 - 2*x - 2*x^2 + 3*x^3 + x^4) / ((1 - x)*(1 - x - x^2)*(1 - x - 3*x^2)). - _Colin Barker_, Feb 22 2018

%e Some solutions for n=8:

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

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

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

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

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

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

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

%Y Cf. A199149.

%K nonn

%O 1,4

%A _R. H. Hardin_, Nov 03 2011

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Last modified April 16 08:27 EDT 2024. Contains 371698 sequences. (Running on oeis4.)