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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
Column 1 is A000244(n-1)
Column 2 is A033890(n-1)
Row 1 is A001906(n-1)
Sequence in context: A248696 A021299 A141678 * A368738 A135477 A182473
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 14 2013
STATUS
approved

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Last modified March 4 05:23 EST 2024. Contains 370522 sequences. (Running on oeis4.)