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

Author

R. H. Hardin, Feb 13 2011

Keywords

• nonn

Comments

Column 2 of A186128.

Examples

			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
		

Links

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

Crossrefs

Cf. A186128.

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