A280309 Number of n X 1 0..2 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, 0, 0, 1, 2, 9, 34, 124, 432, 1464, 4848, 15768, 50528, 159920, 500832, 1554304, 4785664, 14632704, 44465664, 134378112, 404089344, 1209699584, 3606669824, 10713166848, 31713660928, 93585811456, 275367776256, 808068888576

Offset

1,5

Comments

Column 1 of A280313.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 6*a(n-2) - 16*a(n-3) + 12*a(n-4) + 24*a(n-5) + 8*a(n-6) for n>10.

Empirical g.f.: x^4*(1 - 4*x + 3*x^2 + 8*x^3 - 6*x^4 - 12*x^5 - 4*x^6) / (1 - 2*x - 2*x^2)^3. - Colin Barker, Feb 19 2018

Example

All solutions for n=6:
..0. .0. .0. .0. .0. .0. .0. .0. .0
..0. .1. .0. .1. .0. .0. .1. .1. .0
..0. .2. .0. .1. .1. .0. .1. .0. .0
..0. .2. .0. .1. .1. .1. .1. .0. .0
..1. .2. .1. .1. .1. .1. .1. .0. .1
..0. .2. .1. .0. .1. .1. .2. .0. .2

Crossrefs

Cf. A280313.

Sequence in context: A000524 A289614 A120989 * A010763 A077234 A091526

Adjacent sequences: A280306 A280307 A280308 * A280310 A280311 A280312

Keyword

nonn

Author

R. H. Hardin, Dec 31 2016

Status

approved