|
|
A283727
|
|
Number of 2 X n 0..1 arrays with no 1 equal to more than two of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.
|
|
1
|
|
|
0, 0, 10, 60, 242, 1032, 4220, 16376, 62564, 235728, 875630, 3220084, 11746262, 42545240, 153181664, 548710320, 1956760904, 6950669984, 24604072658, 86824376236, 305540509370, 1072522794920, 3756266150212, 13128230615656
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = 6*a(n-1) - 7*a(n-2) - 31*a(n-4) + 14*a(n-5) + 51*a(n-6) + 52*a(n-7) + 12*a(n-8) - 96*a(n-9) - 64*a(n-10).
Empirical g.f.: 2*x^3*(1 - 2*x)*(1 + 2*x)*(5 - 4*x^2) / ((1 + x + 2*x^2)^2*(1 - 4*x + x^2 + 4*x^3)^2). - Colin Barker, Feb 21 2019
|
|
EXAMPLE
|
Some solutions for n=4:
..0..1..1..1. .1..1..0..1. .0..1..0..0. .0..1..1..0. .1..1..1..1
..0..0..0..1. .0..1..1..1. .1..1..1..1. .0..1..0..1. .0..1..0..1
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|