login
A281394
Number of n X 2 0..1 arrays with no element equal to more than two of its horizontal, diagonal or antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
1
0, 0, 6, 36, 160, 676, 2692, 10352, 38868, 143276, 520736, 1871380, 6663484, 23545568, 82661076, 288590204, 1002706896, 3469289876, 11959062188, 41088781264, 140757051348, 480912678028, 1639160372000, 5574818816340
OFFSET
1,3
LINKS
FORMULA
Empirical: a(n) = 6*a(n-1) - 7*a(n-2) - 6*a(n-3) - 5*a(n-4) + 12*a(n-5) + 4*a(n-6) - 4*a(n-8).
Empirical g.f.: 2*x^3*(1 + x - x^2)*(3 - 3*x - x^2) / (1 - 3*x - x^2 + 2*x^4)^2. - Colin Barker, Feb 18 2019
EXAMPLE
Some solutions for n=4:
..0..1. .0..0. .0..0. .0..1. .0..1. .0..1. .0..0. .0..1. .0..0. .0..1
..1..1. .0..1. .0..0. .0..1. .1..1. .0..1. .0..0. .0..1. .0..0. .0..1
..0..1. .1..1. .1..0. .1..1. .0..1. .1..1. .1..0. .0..0. .0..1. .0..0
..1..0. .0..1. .0..1. .0..1. .1..1. .1..1. .0..0. .0..1. .1..1. .0..0
CROSSREFS
Column 2 of A281400.
Sequence in context: A223946 A223919 A263952 * A225380 A371157 A371197
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 21 2017
STATUS
approved