|
|
A281124
|
|
Number of n X 2 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
|
|
1
|
|
|
0, 2, 28, 208, 1364, 8354, 48992, 278966, 1554744, 8524848, 46147848, 247246206, 1313446848, 6927856426, 36320588564, 189426835088, 983467437564, 5085683787674, 26206495324448, 134618732560222, 689572430485168
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = 8*a(n-1) - 8*a(n-2) - 30*a(n-3) - 24*a(n-4) - 8*a(n-5) - a(n-6).
Empirical g.f.: 2*x^2*(1 + x)*(1 + 5*x - 5*x^2 - 3*x^3) / (1 - 4*x - 4*x^2 - x^3)^2. - Colin Barker, Feb 15 2019
|
|
EXAMPLE
|
Some solutions for n=4:
..0..1. .0..1. .0..1. .0..1. .0..1. .0..1. .0..0. .0..0. .0..1. .0..1
..1..0. .1..0. .0..2. .1..0. .1..2. .0..2. .1..2. .1..2. .0..2. .0..1
..1..2. .1..2. .1..2. .0..2. .2..0. .0..1. .0..2. .1..1. .1..2. .2..2
..0..2. .0..0. .1..2. .0..1. .2..0. .1..2. .0..0. .2..0. .2..1. .0..2
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|