A188826 Number of 4 X n binary arrays without the pattern 0 1 diagonally or antidiagonally.

16, 25, 81, 256, 841, 2704, 8836, 28561, 93025, 301401, 980100, 3179089, 10329796, 33524100, 108889225, 353477601, 1147922161, 3726858304, 12101980081, 39292754176, 127587553636, 414263438689, 1345129081209, 4367552437161

Offset

1,1

Comments

Row 4 of A188824.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + 5*a(n-2) - 15*a(n-3) + 3*a(n-4) + 5*a(n-5) - a(n-6) for n>7.

Empirical g.f.: x*(16 - 23*x - 74*x^2 + 128*x^3 - 5*x^4 - 39*x^5 + 7*x^6) / ((1 - 5*x + 6*x^2 - x^3)*(1 + 2*x - x^2 - x^3)). - Colin Barker, Apr 30 2018

Example

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

Crossrefs

Cf. A188824.

Sequence in context: A065408 A112392 A109685 * A152152 A260047 A061101

Adjacent sequences: A188823 A188824 A188825 * A188827 A188828 A188829

Keyword

nonn

Author

R. H. Hardin, Apr 11 2011

Status

approved