|
| |
|
|
A231855
|
|
T(n,k)=Number of nXk 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions)
|
|
13
|
|
|
|
1, 1, 3, 3, 8, 9, 8, 34, 55, 27, 21, 144, 656, 377, 81, 55, 612, 7339, 12404, 2584, 243, 144, 2613, 85288, 360966, 234336, 17711, 729, 377, 11159, 991167, 11149456, 17726611, 4426924, 121393, 2187, 987, 47675, 11529929, 342945563, 1454768048, 870478586
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,3
|
|
|
COMMENTS
|
Table starts
....1......1..........3.............8...............21..................55
....3......8.........34...........144..............612................2613
....9.....55........656..........7339............85288..............991167
...27....377......12404........360966.........11149456...........342945563
...81...2584.....234336......17726611.......1454768048........118292347982
..243..17711....4426924.....870478586.....189801034186......40798265169064
..729.121393...83630516...42745416641...24762957054535...14071005227913420
.2187.832040.1579892344.2099041399895.3230773305296573.4852980371902817445
|
|
|
LINKS
|
|
|
|
FORMULA
|
Empirical for column k:
k=1: a(n) = 3*a(n-1)
k=2: a(n) = 7*a(n-1) -a(n-2)
k=3: a(n) = 21*a(n-1) -41*a(n-2) +22*a(n-3) for n>4
k=4: [order 9] for n>10
k=5: [order 21] for n>22
k=6: [order 52] for n>54
Empirical for row n:
n=1: a(n) = 3*a(n-1) -a(n-2) for n>3
n=2: [order 8] for n>9
n=3: [order 35] for n>39
|
|
|
EXAMPLE
|
Some solutions for n=3 k=4
..0..0..0..1....0..0..2..1....0..0..0..0....0..0..0..1....0..0..1..0
..0..2..2..2....1..2..1..1....1..1..1..1....0..0..2..2....0..2..0..1
..2..0..0..0....1..1..2..2....1..2..0..0....1..0..0..0....2..2..2..2
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
