A282185 Number of n X 2 0..2 arrays with no element equal to more than four of its king-move neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

0, 0, 1, 8, 104, 1222, 13552, 144784, 1506870, 15382464, 154705344, 1537619888, 15136209536, 147816712064, 1433881609384, 13829678601088, 132726827340160, 1268315293540128, 12073757901185280, 114548957745270528

Offset

1,4

Links

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

Formula

Empirical: a(n) = 16*a(n-1) - 48*a(n-2) - 116*a(n-3) - 160*a(n-4) - 96*a(n-5) - 36*a(n-6) for n>9.

Empirical g.f.: x^3*(1 - 8*x + 24*x^2 + 58*x^3 + 80*x^4 + 48*x^5 + 18*x^6) / (1 - 8*x - 8*x^2 - 6*x^3)^2. - Colin Barker, Feb 20 2019

Example

All solutions for n=4:
..0..0. .0..0. .0..0. .0..1. .0..0. .0..0. .0..1. .0..1
..1..1. .0..0. .0..0. .2..2. .0..0. .0..0. .1..1. .0..0
..1..1. .0..0. .0..0. .2..2. .0..0. .0..0. .1..1. .0..0
..1..1. .0..1. .1..1. .2..2. .1..2. .1..0. .1..1. .0..0

Crossrefs

Column 2 of A282189.

Sequence in context: A335608 A109774 A001657 * A354064 A106260 A112121

Adjacent sequences: A282182 A282183 A282184 * A282186 A282187 A282188

Keyword

nonn

Author

R. H. Hardin, Feb 08 2017

Status

approved