A188748 Number of 3 X n binary arrays without the pattern 1 1 1 diagonally, vertically or antidiagonally.
7, 49, 292, 1723, 10327, 61996, 371641, 2227333, 13350748, 80027347, 479695855, 2875358812, 17235289777, 103310698477, 619258487404, 3711920099323, 22249757087527, 133368089673676, 799426585401961, 4791872379016597
Offset: 1
Keywords
Examples
Some solutions for 3 X 3: ..0..1..1....0..0..1....1..0..0....1..0..0....0..0..1....1..1..0....0..1..0 ..1..0..0....1..0..0....0..1..1....1..0..1....1..0..1....1..0..0....1..1..0 ..0..0..0....0..0..0....1..0..0....0..0..0....1..0..0....0..1..1....0..0..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..200
Formula
Empirical: a(n) = 6*a(n-1) -2*a(n-2) +11*a(n-3) +10*a(n-4) -30*a(n-5) -12*a(n-6).
Empirical g.f.: x*(7 + 7*x + 12*x^2 - 8*x^3 - 36*x^4 - 12*x^5) / (1 - 6*x + 2*x^2 - 11*x^3 - 10*x^4 + 30*x^5 + 12*x^6). - Colin Barker, Feb 20 2018
Comments