A281982 Number of n X 2 0..1 arrays with no element unequal to more than four of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 2, 16, 88, 432, 2008, 8992, 39200, 167552, 705440, 2934784, 12091264, 49416448, 200598912, 809606656, 3251253760, 12999782400, 51779385856, 205542608896, 813446920192, 3210502631424, 12640023828480, 49653803819008

Offset

1,3

Links

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

Formula

Empirical: a(n) = 8*a(n-1) - 20*a(n-2) + 24*a(n-3) - 36*a(n-4) + 16*a(n-5) - 16*a(n-6).

Empirical g.f.: 2*x^3 / (1 - 4*x + 2*x^2 - 4*x^3)^2. - Colin Barker, Feb 20 2019

Example

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

Crossrefs

Column 2 of A281988.

Sequence in context: A370192 A069440 A000431 * A207595 A253487 A207019

Adjacent sequences: A281979 A281980 A281981 * A281983 A281984 A281985

Keyword

nonn

Author

R. H. Hardin, Feb 04 2017

Status

approved