A188861 Number of n X 4 binary arrays without the pattern 0 1 diagonally, vertically or antidiagonally.

16, 41, 68, 95, 122, 149, 176, 203, 230, 257, 284, 311, 338, 365, 392, 419, 446, 473, 500, 527, 554, 581, 608, 635, 662, 689, 716, 743, 770, 797, 824, 851, 878, 905, 932, 959, 986, 1013, 1040, 1067, 1094, 1121, 1148, 1175, 1202, 1229, 1256, 1283, 1310, 1337, 1364

Offset: 1

Author

R. H. Hardin, Apr 12 2011

Keywords

• nonn

Comments

Column 4 of A188866.

Examples

			Some solutions for 3 X 4:
..1..1..1..1....1..1..0..1....1..1..1..1....1..0..1..1....1..1..1..1
..1..1..1..1....0..0..0..0....1..1..1..0....0..0..0..0....0..0..1..0
..1..0..0..1....0..0..0..0....1..1..0..0....0..0..0..0....0..0..0..0
		

Links

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

Crossrefs

Cf. A188866.

Programs

Mathematica

Join[{16}, Range[41, 7000, 27]] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)

Formula

Empirical: a(n) = 27*n - 13 for n>1.

Conjectures from Colin Barker, Feb 28 2018: (Start)

G.f.: x*(16 + 9*x + 2*x^2) / (1 - x)^2.

a(n) = 2*a(n-1) - a(n-2) for n>3.

(End)