|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|