A281050 Number of n X 2 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, 1, 6, 29, 122, 468, 1686, 5807, 19338, 62731, 199264, 622152, 1914780, 5821645, 17515566, 52221929, 154461110, 453654108, 1324053522, 3842768987, 11096398578, 31895230903, 91296545404, 260329675536, 739725018360, 2095147333465

Offset

1,3

Links

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

Formula

Empirical: a(n) = 9*a(n-1) - 30*a(n-2) + 45*a(n-3) - 30*a(n-4) + 9*a(n-5) - a(n-6).

Empirical g.f.: x^2*(1 - 3*x + 5*x^2 - 4*x^3) / (1 - 3*x + x^2)^3. - Colin Barker, Feb 15 2019

Example

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

Crossrefs

Column 2 of A281056.

Sequence in context: A184130 A326805 A061648 * A267774 A243474 A111644

Adjacent sequences: A281047 A281048 A281049 * A281051 A281052 A281053

Keyword

nonn

Author

R. H. Hardin, Jan 13 2017

Status

approved