A205221 Number of (n+1) X 4 0..1 arrays with the number of equal 2 X 2 subblock diagonal pairs and equal antidiagonal pairs differing from each horizontal or vertical neighbor, and new values 0..1 introduced in row major order.

52, 132, 328, 824, 2072, 5176, 13032, 32488, 81816, 203864, 513256, 1279208, 3218968, 8026968, 20187368, 50370024, 126607000, 316079576, 794071656, 1983434984, 4980636824, 12446080472, 31241340648, 78097719912, 195970301464

Offset

1,1

Comments

Column 3 of A205226.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = a(n-1) +12*a(n-2) -11*a(n-3) -47*a(n-4) +40*a(n-5) +64*a(n-6) -48*a(n-7) -8*a(n-8) for n>9.

Empirical g.f.: 4*x*(13 + 20*x - 107*x^2 - 129*x^3 + 302*x^4 + 237*x^5 - 284*x^6 - 52*x^7 + 16*x^8) / (1 - x - 12*x^2 + 11*x^3 + 47*x^4 - 40*x^5 - 64*x^6 + 48*x^7 + 8*x^8). - Colin Barker, Jun 11 2018

Example

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

Crossrefs

Cf. A205226.

Sequence in context: A346898 A120534 A122166 * A044303 A044684 A346882

Adjacent sequences: A205218 A205219 A205220 * A205222 A205223 A205224

Keyword

nonn

Author

R. H. Hardin, Jan 23 2012

Status

approved