|
|
A269685
|
|
Number of length-n 0..3 arrays with no repeated value differing from the previous repeated value by plus or minus one modulo 3+1.
|
|
1
|
|
|
4, 16, 64, 248, 944, 3544, 13168, 48536, 177776, 647896, 2351728, 8508440, 30701168, 110537560, 397266544, 1425629336, 5109684848, 18295104472, 65449056880, 233970500888, 835908980336, 2984966034520, 10654610339440, 38017445912984
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = 6*a(n-1) - 7*a(n-2) - 6*a(n-3).
G.f.: 4*x*(1 - 2*x - x^2) / ((1 - 3*x)*(1 - 3*x - 2*x^2)).
a(n) = 2^(-n)*(-17*2^(2+n)*3^n + (51-15*sqrt(17))*(3-sqrt(17))^n + 3*(3+sqrt(17))^n*(17+5*sqrt(17))) / 51.
(End)
|
|
EXAMPLE
|
Some solutions for n=9:
..1. .0. .1. .2. .0. .2. .0. .1. .0. .0. .1. .0. .0. .0. .1. .0
..2. .3. .3. .0. .3. .0. .3. .0. .1. .3. .1. .1. .0. .1. .0. .2
..0. .1. .0. .3. .2. .1. .0. .2. .2. .0. .1. .2. .2. .3. .0. .3
..0. .2. .0. .0. .1. .0. .2. .2. .3. .2. .2. .3. .2. .2. .3. .1
..0. .1. .1. .1. .3. .1. .2. .0. .1. .2. .3. .2. .2. .1. .1. .3
..2. .1. .2. .3. .0. .0. .1. .2. .1. .1. .1. .1. .0. .2. .3. .3
..0. .3. .1. .2. .2. .0. .3. .1. .0. .2. .3. .0. .0. .0. .0. .0
..0. .1. .0. .1. .3. .3. .1. .3. .1. .2. .2. .1. .2. .1. .0. .1
..3. .3. .0. .2. .3. .1. .0. .0. .2. .1. .1. .3. .2. .2. .2. .3
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|