A196141 - OEIS

%I #11 Jan 21 2019 17:46:52

%S 4,8,7,26,49,85,178,348,683,1349,2688,5319,10498,20818,41206,81574,

%T 161646,320215,634294,1256481,2489029,4930656,9767642,19350237,

%U 38333645,75940498,150441579,298031468,590414638,1169642000,2317123308,4590345948

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

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

%C Column 3 of A196146.

%H R. H. Hardin, <a href="/A196141/b196141.txt">Table of n, a(n) for n = 1..200</a>

%H Robert Israel, <a href="/A196141/a196141.pdf">Maple-assisted proof of empirical recurrence</a>

%F Empirical: a(n) = 3*a(n-1) -2*a(n-2) +a(n-3) -3*a(n-4) +3*a(n-5) -a(n-6) -7*a(n-8) +a(n-9) +4*a(n-10) +2*a(n-11) +6*a(n-12).

%F Empirical g.f.: x*(4 - 4*x - 9*x^2 + 17*x^3 - 11*x^4 - 5*x^5 - 4*x^6 + 14*x^8 + 4*x^9 + 12*x^10) / (1 - 3*x + 2*x^2 - x^3 + 3*x^4 - 3*x^5 + x^6 + 7*x^8 - x^9 - 4*x^10 - 2*x^11 - 6*x^12). - _Colin Barker_, May 08 2018

%F Empirical formulas verified: see link. - _Robert Israel_, Jan 21 2019

%e Some solutions for n=4:

%e .0.1.1...1.1.0...0.0.0...1.0.0...1.0.1...0.0.1...0.0.1

%e .1.1.0...0.1.1...1.1.1...3.1.1...1.0.1...0.0.1...1.1.1

%e .3.1.1...1.1.3...1.1.3...1.1.1...1.0.1...0.0.1...1.1.0

%e .1.0.1...1.0.1...0.0.1...0.0.0...1.0.1...0.0.1...0.1.1

%Y Cf. A196146.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 28 2011