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A197666 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,0,1 for x=0,1,2,3,4. 1

%I #8 May 14 2018 05:56:54

%S 3,9,22,71,217,642,1963,5963,18018,54753,166329,504940,1534985,

%T 4667983,14198968,43215503,131584139,400800484,1221337807,3723140135,

%U 11353757744,34635822651,105696236527,322652635812,985253141189,3009481166143

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

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

%C Column 2 of A197672.

%H R. H. Hardin, <a href="/A197666/b197666.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 3*a(n-1) +4*a(n-2) -25*a(n-4) -37*a(n-5) +4*a(n-6) +23*a(n-7) +17*a(n-8) -5*a(n-9) -a(n-10).

%F Empirical g.f.: x*(1 - x)*(1 + x)^2*(3 - 3*x - 11*x^2 - 20*x^3 - 3*x^4 + 15*x^5 + 2*x^6) / ((1 - x - 5*x^2 - 4*x^3 - x^4 + x^5)*(1 - 2*x - x^2 - 7*x^3 + 6*x^4 + x^5)). - _Colin Barker_, May 14 2018

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A197672.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 17 2011

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Last modified February 22 05:23 EST 2024. Contains 370239 sequences. (Running on oeis4.)