A281051 Number of n X 3 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

0, 6, 68, 376, 1492, 4988, 15028, 42252, 113076, 291660, 731060, 1791052, 4306868, 10197068, 23828404, 55060556, 125999028, 285894732, 643864500, 1440442444, 3203438516, 7086237772, 15599703988, 34190878796, 74638727092, 162339448908

Offset

1,2

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 6*a(n-2) - 4*a(n-3) + 8*a(n-4) for n>6.

Empirical g.f.: 2*x^2*(3 + x)*(1 + 2*x)*(1 + 4*x + 2*x^2) / ((1 + x)*(1 - 2*x)^3). - Colin Barker, Feb 15 2019

Example

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

Crossrefs

Column 3 of A281056.

Sequence in context: A152390 A200059 A183470 * A006737 A128869 A186669

Adjacent sequences: A281048 A281049 A281050 * A281052 A281053 A281054

Keyword

nonn

Author

R. H. Hardin, Jan 13 2017

Status

approved