A231908 T(n,k)=Number of nXk 0..2 arrays with no element having a strict majority of its horizontal, diagonal 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, 17, 9, 8, 137, 74, 27, 21, 948, 1740, 315, 81, 55, 6975, 31167, 22759, 1343, 243, 144, 50323, 614818, 1082472, 297099, 5734, 729, 377, 366170, 11900005, 57946241, 37368831, 3882566, 24495, 2187, 987, 2657785, 232002949, 3045772177

Offset

1,3

Comments

Table starts

....1......1.........3.............8...............21...................55

....3.....17.......137...........948.............6975................50323

....9.....74......1740.........31167...........614818.............11900005

...27....315.....22759.......1082472.........57946241...........3045772177

...81...1343....297099......37368831.......5429359691.........773715251151

..243...5734...3882566....1291573433.....509273459716......196795864115357

..729..24495..50739125...44640322903...47773200503463....50062652312668838

.2187.104655.663117735.1542901809201.4481443113541663.12735271817562619233

Links

R. H. Hardin, Table of n, a(n) for n = 1..96

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1)

k=2: a(n) = 6*a(n-1) -8*a(n-2) +2*a(n-3) +3*a(n-4) -a(n-5) for n>6

k=3: [order 17] for n>18

k=4: [order 81] for n>82

Empirical for row n:

n=1: a(n) = 3*a(n-1) -a(n-2) for n>3

n=2: a(n) = 9*a(n-1) -5*a(n-2) -66*a(n-3) +78*a(n-4) +4*a(n-5) -16*a(n-6)

n=3: [order 37] for n>38

Example

Some solutions for n=3 k=4
..0..0..2..1....0..0..0..1....0..2..0..1....0..2..2..1....0..0..0..0
..1..0..1..1....2..1..0..0....2..2..2..0....2..2..1..2....0..0..1..0
..0..2..0..0....1..2..2..1....2..0..0..2....2..0..0..1....1..1..0..2

Crossrefs

Column 1 is A000244(n-1)

Column 2 is A231779

Row 1 is A001906(n-1)

Sequence in context: A127539 A342837 A278627 * A226610 A332840 A279172

Adjacent sequences: A231905 A231906 A231907 * A231909 A231910 A231911

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 15 2013

Status

approved