|
|
A232670
|
|
Number of (n+1) X (1+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally, vertically, diagonally or antidiagonally.
|
|
1
|
|
|
36, 212, 1568, 11878, 87680, 651678, 4846056, 35990386, 267429284, 1987124934, 14763908592, 109698051138, 815067420300, 6055993810126, 44996556671640, 334327945984154, 2484081968889732, 18456924487924070, 137136383652862288
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = 2*a(n-1) + 21*a(n-2) + 118*a(n-3) + 170*a(n-4) + 166*a(n-5) - 52*a(n-6) - 48*a(n-7) - 64*a(n-8).
Empirical g.f.: 2*x*(18 + 70*x + 194*x^2 + 21*x^3 - 70*x^4 - 80*x^5 - 32*x^6) / (1 - 2*x - 21*x^2 - 118*x^3 - 170*x^4 - 166*x^5 + 52*x^6 + 48*x^7 + 64*x^8). - Colin Barker, Oct 05 2018
|
|
EXAMPLE
|
Some solutions for n=5:
..2..1....0..2....2..1....1..2....0..2....2..1....1..2....1..2....0..2....0..1
..1..0....0..1....1..0....1..0....1..0....1..0....2..0....0..1....1..2....2..1
..2..0....2..0....2..0....1..0....2..2....0..0....0..0....0..0....2..1....1..1
..0..2....2..0....2..1....0..2....2..1....2..1....1..0....2..1....0..1....0..2
..0..1....1..0....2..0....0..2....0..1....2..0....1..2....0..1....1..1....1..2
..2..2....0..2....2..1....0..1....2..2....1..0....2..0....1..2....2..2....2..0
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|