A259214 Number of (n+1)X(n+1) 0..1 arrays with each 2X2 subblock having clockwise pattern 0000 0011 or 0101.

7, 23, 66, 183, 487, 1278, 3319, 8591, 22210, 57455, 148815, 386046, 1002991, 2609559, 6797794

Offset: 1

Author

R. H. Hardin, Jun 21 2015

Keywords

• nonn

Comments

Diagonal of A259222

Examples

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

Crossrefs

Cf. A259222

Formula

Empirical: a(n) = 6*a(n-1) -10*a(n-2) -2*a(n-3) +16*a(n-4) -6*a(n-5) -5*a(n-6) +2*a(n-7)

Empirical g.f: -x*(7-19*x-2*x^2+31*x^3-17*x^4-8*x^5+4*x^6)/(x-1)/(2*x-1)/(1+x)/(x^2-3*x+1)/(x^2+x-1) . - R. J. Mathar, Nov 09 2018

Empirical: a(n) = 18*A001906(n+1)/5 -7*A001906(n)/5 +2 + 4*2^n - 4*A000045(n+3)+2*(-1)^n /5. - R. J. Mathar, Nov 09 2018