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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

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

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 * A135477 A182473 A335602

Adjacent sequences:  A231852 A231853 A231854 * A231856 A231857 A231858

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Nov 14 2013

STATUS

approved

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Last modified September 19 00:22 EDT 2021. Contains 347549 sequences. (Running on oeis4.)