A208003 Number of n X 4 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 1 1 and 1 1 0 vertically.

9, 81, 221, 536, 1711, 4993, 16742, 53411, 182247, 608142, 2095301, 7157363, 24822376, 85845073, 299033933, 1040987192, 3636447903, 12703622001, 44454269798, 155590727603, 545028524023, 1909557999406, 6693157243061

Offset

1,1

Comments

Column 4 of A208007.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 6*a(n-1) - 3*a(n-2) - 36*a(n-3) + 54*a(n-4) + 24*a(n-5) - 69*a(n-6) + 12*a(n-7) + 19*a(n-8) - 6*a(n-9) for n>10.

G.f.: x*(9 + 27*x - 238*x^2 - 223*x^3 + 1588*x^4 - 299*x^5 - 2044*x^6 + 767*x^7 + 603*x^8 - 234*x^9) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)*(1 - x - x^2)*(1 - 2*x - 7*x^2 + 6*x^3)). - Colin Barker, Jun 26 2018

Example

Some solutions for n=4:
..1..0..1..1....0..1..0..1....1..1..1..0....1..1..1..0....1..1..0..1
..0..1..1..0....0..0..0..0....0..0..0..0....1..0..1..1....0..1..0..1
..1..0..1..1....0..1..0..1....1..1..1..0....1..1..1..0....0..1..1..1
..0..1..1..0....0..0..0..0....0..0..0..0....1..0..1..1....0..1..0..1

Crossrefs

Cf. A208007.

Sequence in context: A207662 A207484 A207265 * A207881 A207565 A207758

Adjacent sequences: A208000 A208001 A208002 * A208004 A208005 A208006

Keyword

nonn

Author

R. H. Hardin, Feb 22 2012

Status

approved