login
A232031
Number of (n+1) X (1+1) 0..1 arrays with every element equal to some horizontal, vertical or antidiagonal neighbor, with top left element zero.
4
3, 11, 37, 129, 450, 1568, 5464, 19041, 66354, 231230, 805789, 2808009, 9785334, 34099877, 118831060, 414101811, 1443059667, 5028766229, 17524216333, 61068290730, 212810436816, 741600615908, 2584325664397, 9005843571858
OFFSET
1,1
COMMENTS
Column 1 of A232038.
LINKS
FORMULA
Empirical: a(n) = 4*a(n-1) - 2*a(n-2) + a(n-3) - a(n-4).
Empirical g.f.: x*(3 - x - x^2) / (1 - 4*x + 2*x^2 - x^3 + x^4). - Colin Barker, Mar 19 2018
EXAMPLE
Some solutions for n=7:
..0..0....0..0....0..0....0..1....0..0....0..0....0..0....0..0....0..1....0..0
..0..0....0..0....0..1....0..1....1..1....1..1....0..1....0..0....0..1....0..0
..0..0....1..1....1..0....0..0....1..0....1..0....0..1....0..1....1..1....0..0
..0..0....0..0....0..1....0..0....0..1....1..0....1..0....0..1....1..0....1..1
..1..1....1..1....1..1....1..1....1..0....0..1....1..0....1..1....0..0....1..0
..1..0....0..0....1..1....0..1....1..0....1..1....0..0....1..0....1..0....1..0
..0..0....1..1....1..0....0..0....1..1....0..0....0..1....0..1....1..1....0..0
..1..1....0..0....1..0....0..0....0..0....1..1....0..1....0..1....0..0....0..0
CROSSREFS
Cf. A232038.
Sequence in context: A046722 A214996 A180168 * A047102 A109000 A183511
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 17 2013
STATUS
approved