|
|
A279735
|
|
Number of n X 2 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
|
|
1
|
|
|
0, 2, 8, 26, 80, 240, 708, 2062, 5944, 16990, 48220, 136032, 381768, 1066586, 2968040, 8230370, 22751528, 62716752, 172447884, 473081830, 1295113240, 3538749862, 9652296628, 26285128896, 71472896400, 194075990450, 526312559048
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4).
G.f.: 2*x^2*(1 - 2*x) / (1 - 3*x + x^2)^2.
a(n) = (-1)*(2^(1-n)*(sqrt(5)*((3-sqrt(5))^n-(3+sqrt(5))^n) + 5*(3-sqrt(5))^n*(2+sqrt(5))*n - 5*(-2+sqrt(5))*(3+sqrt(5))^n*n)) / 25.
(End)
|
|
EXAMPLE
|
Some solutions for n=4:
..0..1. .0..0. .0..1. .0..1. .0..1. .0..0. .0..1. .0..0. .0..1. .0..1
..0..1. .1..1. .0..0. .0..1. .0..0. .1..0. .1..0. .1..0. .0..0. .0..1
..1..0. .0..1. .1..1. .1..1. .0..1. .1..1. .1..1. .1..0. .1..0. .0..0
..1..1. .0..1. .1..0. .0..1. .1..0. .0..1. .1..0. .1..0. .1..1. .1..1
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|