A196952 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,3,4,0 for x=0,1,2,3,4.

3, 9, 26, 87, 282, 919, 2987, 9722, 31643, 102962, 335048, 1090310, 3548040, 11545789, 37571671, 122263766, 397863990, 1294706917, 4213164246, 13710247872, 44615134395, 145184117131, 472450174347, 1537421386475, 5002992156783

Offset: 1

Author

R. H. Hardin, Oct 08 2011

Keywords

• nonn

Comments

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

Column 3 of A196957.

Examples

			Some solutions for n=4:
..1..1..0....1..0..0....0..0..1....0..1..1....0..0..0....0..1..1....0..0..0
..0..0..0....1..0..1....0..0..1....0..0..0....1..1..0....1..0..0....0..1..1
..0..0..0....0..0..1....1..1..0....1..0..1....0..0..0....1..0..0....0..0..0
..0..0..0....0..0..0....0..0..0....1..0..1....0..0..0....0..0..0....0..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A196957.

Formula

Empirical: a(n) = a(n-1) +4*a(n-2) +8*a(n-3) +10*a(n-4) +a(n-5) -9*a(n-6) -6*a(n-7) +a(n-9) for n>10.

Empirical g.f.: x*(3 + 6*x + 5*x^2 + x^3 - 11*x^4 - 12*x^5 + 2*x^6 + 6*x^7 + 2*x^8 - x^9) / (1 - x - 4*x^2 - 8*x^3 - 10*x^4 - x^5 + 9*x^6 + 6*x^7 - x^9). - Colin Barker, May 10 2018