|
|
A183357
|
|
One quarter the number of n X 5 1..4 arrays with no two neighbors of any element equal to each other.
|
|
1
|
|
|
108, 2304, 3888, 9216, 24192, 57600, 137088, 331776, 802944, 1937664, 4675968, 11289600, 27257472, 65804544, 158864256, 383533056, 925932672, 2235398400, 5396727168, 13028852736, 31454434944, 75937722624, 183329877888
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = 2*a(n-1) + 2*a(n-3) + a(n-4) for n>7.
Empirical g.f.: 36*x*(3 + 58*x - 20*x^2 + 34*x^3 + 29*x^4 - 24*x^5 - 12*x^6) / ((1 + x^2)*(1 - 2*x - x^2)). - Colin Barker, Mar 28 2018
|
|
EXAMPLE
|
Some solutions for 7 X 5 with a(1,1)=1:
..1..1..2..4..1....1..2..2..3..3....1..2..2..3..3....1..1..3..4..1
..4..3..3..4..2....1..4..4..1..2....3..4..4..1..1....4..2..2..4..3
..2..2..1..1..3....2..3..3..1..2....2..1..3..2..2....3..3..1..1..2
..3..4..4..2..3....4..1..2..4..4....2..1..3..4..4....2..4..4..3..2
..1..1..3..2..1....3..1..2..3..3....3..4..2..1..1....1..1..2..3..1
..4..2..3..4..4....2..4..4..1..2....3..4..2..3..3....4..3..2..4..1
..3..2..1..1..2....2..3..3..1..4....2..1..1..4..2....2..3..1..4..2
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|