|
|
A297219
|
|
Number of n X 3 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 1 neighboring 1s.
|
|
1
|
|
|
3, 8, 24, 68, 196, 564, 1620, 4660, 13396, 38516, 110740, 318388, 915412, 2631924, 7567124, 21756468, 62552660, 179847028, 517083540, 1486682292, 4274404564, 12289467892, 35333815316, 101589305140, 292082437972, 839774919796
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = a(n-1) + 4*a(n-2) + 4*a(n-3).
Empirical g.f.: x*(3 + 5*x + 4*x^2) / (1 - x - 4*x^2 - 4*x^3). - Colin Barker, Feb 26 2019
|
|
EXAMPLE
|
Some solutions for n=7:
..0..0..0. .0..1..1. .1..1..0. .0..0..0. .0..1..0. .1..1..0. .1..1..0
..1..1..0. .0..0..1. .0..0..0. .0..1..1. .1..0..1. .0..0..0. .0..0..0
..0..0..0. .0..1..0. .0..1..0. .0..0..0. .0..1..0. .0..1..1. .1..1..0
..0..1..0. .0..1..1. .1..0..0. .1..1..0. .0..0..0. .0..0..0. .0..0..0
..1..0..0. .0..0..0. .1..1..0. .0..1..1. .0..1..1. .0..1..0. .0..1..1
..0..1..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .1..0..0. .0..0..1
..1..0..0. .0..0..0. .0..0..0. .0..1..1. .1..1..0. .0..1..1. .0..1..0
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|