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A196630 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 1,3,2,0,4 for x=0,1,2,3,4. 3

%I #8 Feb 22 2018 11:04:38

%S 1,2,5,10,26,65,161,403,1006,2511,6270,15654,39083,97579,243625,

%T 608258,1518637,3791578,9466426,23634809,59008985,147327627,367832622,

%U 918367047,2292885358,5724642758,14292705299,35684571667,89093606033,222439846274

%N Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 1,3,2,0,4 for x=0,1,2,3,4.

%C Every 0 is next to 0 1's, every 1 is next to 1 3's, every 2 is next to 2 2's, every 3 is next to 3 0's, every 4 is next to 4 4's.

%C Column 2 of A196636.

%H R. H. Hardin, <a href="/A196630/b196630.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) + a(n-2) + a(n-3) - a(n-4).

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

%e All solutions for n=4:

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

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

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

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

%Y Cf. A196636.

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 04 2011

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