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

1,1

Comments

Column 4 of A188866.

Links

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

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)

Example

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

Mathematica

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

Crossrefs

Cf. A188866.

Sequence in context: A246344 A044093 A044474 * A134593 A227816 A200408

Adjacent sequences: A188858 A188859 A188860 * A188862 A188863 A188864

Keyword

nonn

Author

R. H. Hardin, Apr 12 2011

Status

approved