A280549 Number of n X 3 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

0, 9, 50, 144, 325, 670, 1316, 2502, 4654, 8521, 15412, 27612, 49085, 86695, 152282, 266222, 463487, 803970, 1390026, 2396244, 4119894, 7066303, 12093158, 20654128, 35209707, 59919341, 101806274, 172716156, 292607401, 495074182, 836609600

Offset: 1

Author

R. H. Hardin, Jan 05 2017

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 3 of A280554.

Formula

Empirical: a(n) = 5*a(n-1) - 7*a(n-2) - 2*a(n-3) + 10*a(n-4) - 2*a(n-5) - 5*a(n-6) + a(n-7) + a(n-8) for n>10.

Empirical g.f.: x^2*(9 + 5*x - 43*x^2 - 27*x^3 + 63*x^4 + 47*x^5 - 33*x^6 - 25*x^7 + 8*x^8) / ((1 - x)^2*(1 - x - x^2)^3). - Colin Barker, Feb 13 2019