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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.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 23 2012
STATUS
approved