A186121 Number of (n+1) X 3 binary arrays with every 2 X 2 subblock diagonal sum less antidiagonal sum equal to some horizontal or vertical neighbor 2 X 2 subblock diagonal sum less antidiagonal sum.

14, 38, 94, 254, 682, 1878, 5214, 14606, 41138, 116350, 330046, 938174, 2670826, 7611430, 21707790, 61943694, 176825074, 504902766, 1441965358, 4118707422, 11765461418, 33611411190, 96025298558, 274346613774, 783834214130

Offset

1,1

Comments

Column 2 of A186128.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 3*a(n-2) - 13*a(n-3) + 6*a(n-4) + 14*a(n-5) + 6*a(n-6) + 8*a(n-7) - 16*a(n-8) - 16*a(n-9).

Empirical g.f.: 2*x*(7 - 16*x - 27*x^2 + 40*x^3 + 52*x^4 + 14*x^5 - 4*x^6 - 72*x^7 - 64*x^8) / ((1 - 2*x)*(1 - 3*x - 3*x^2 + 7*x^3 + 8*x^4 + 2*x^5 - 2*x^6 - 12*x^7 - 8*x^8)). - Colin Barker, Apr 17 2018

Example

Some solutions for 5 X 3:
..0..1..1....0..0..1....1..0..0....0..0..1....0..0..1....0..1..1....0..0..1
..1..1..1....0..0..1....1..1..1....1..1..1....1..0..0....1..1..0....1..1..1
..1..0..0....1..0..0....0..1..1....1..1..0....0..0..1....1..1..1....1..1..0
..0..0..1....0..0..0....0..0..0....1..1..1....0..0..1....0..0..1....1..1..0
..0..0..1....0..1..1....1..0..0....0..0..1....0..0..1....0..0..1....0..1..1

Crossrefs

Cf. A186128.

Sequence in context: A256560 A058826 A142241 * A231391 A231459 A244702

Adjacent sequences: A186118 A186119 A186120 * A186122 A186123 A186124

Keyword

nonn

Author

R. H. Hardin, Feb 13 2011

Status

approved