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A197211 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,3,2,1,0 for x=0,1,2,3,4. 4

%I #8 Feb 22 2018 11:16:00

%S 1,2,5,8,18,37,73,151,306,621,1266,2572,5231,10641,21637,44006,89497,

%T 182008,370158,752797,1530977,3113587,6332166,12877865,26190002,

%U 53263176,108322495,220297841,448024553,911157386,1853040797,3768569784

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

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

%C Column 2 of A197217.

%H R. H. Hardin, <a href="/A197211/b197211.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = a(n-1) + a(n-2) + 2*a(n-3) + a(n-5).

%F Empirical g.f.: x*(1 + x + 2*x^2 - x^3 + x^4) / (1 - x - x^2 - 2*x^3 - x^5). - _Colin Barker_, Feb 22 2018

%e All solutions for n=4:

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

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

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

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

%Y Cf. A197217.

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 11 2011

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Last modified March 28 05:01 EDT 2024. Contains 371235 sequences. (Running on oeis4.)