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

1,1

Comments

Diagonal of A259222

Links

Table of n, a(n) for n=1..15.

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

Example

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

Sequence in context: A365439 A266801 A066187 * A114246 A297315 A048457

Adjacent sequences: A259211 A259212 A259213 * A259215 A259216 A259217

Keyword

nonn

Author

R. H. Hardin, Jun 21 2015

Status

approved