A196212 - OEIS

%I #8 Feb 22 2018 09:36:42

%S 3,9,20,61,189,544,1629,4973,15040,45739,140129,429448,1318027,

%T 4054639,12485046,38469569,118629261,366006920,1129623099,3487480563,

%U 10769378230,33261326067,102741225843,317390237024,980560274021,3029559578685

%N Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,2,4 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 1's, every 3 is next to 3 2's, every 4 is next to 4 4's.

%C Column 2 of A196218.

%H R. H. Hardin, <a href="/A196212/b196212.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) +4*a(n-2) +6*a(n-3) -8*a(n-4) -39*a(n-5) -33*a(n-6) -17*a(n-7) +5*a(n-8) +8*a(n-9) +a(n-10).

%F Empirical g.f.: x*(1 + x)^2*(3 - 3*x - 7*x^2 - 16*x^3 - 4*x^4 + 15*x^5 + 3*x^6) / ((1 - x - 7*x^3 - x^4)*(1 - x - 5*x^2 - 4*x^3 - 2*x^4 + x^5 + x^6)). - _Colin Barker_, Feb 22 2018

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A196218.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 29 2011