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).

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

Offset: 1

Author

R. H. Hardin, Nov 14 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..161

Crossrefs

Column 1 is A000244(n-1)

Column 2 is A033890(n-1)

Row 1 is A001906(n-1)

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