|
|
A280955
|
|
Number of n X 2 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
|
|
1
|
|
|
2, 9, 42, 205, 997, 4850, 23593, 114769, 558298, 2715861, 13211405, 64267362, 312630929, 1520804569, 7398009354, 35987886621, 175064388469, 851607109714, 4142673879353, 20152188344737, 98031056006074, 476875651282597
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = 4*a(n-1) + 4*a(n-2) + a(n-3) for n>4.
Empirical g.f.: x*(1 - x)*(1 + x)*(2 + x) / (1 - 4*x - 4*x^2 - x^3). - 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
..0..2. .2..0. .1..2. .2..1. .2..2. .2..2. .1..1. .1..2. .2..2. .2..0
..1..0. .1..2. .0..2. .0..2. .1..0. .1..0. .2..2. .2..0. .1..0. .0..1
..0..1. .0..0. .1..1. .1..0. .1..0. .2..2. .0..1. .1..1. .0..2. .2..1
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|