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

1,2

Links

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

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

Example

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

Crossrefs

Column 3 of A280554.

Sequence in context: A080812 A276239 A116169 * A084367 A006974 A279979

Adjacent sequences: A280546 A280547 A280548 * A280550 A280551 A280552

Keyword

nonn

Author

R. H. Hardin, Jan 05 2017

Status

approved