A231785 T(n,k)=Number of nXk 0..2 arrays with no element having a strict majority of its horizontal and vertical neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions)

1, 1, 1, 3, 17, 3, 8, 74, 74, 8, 21, 315, 854, 315, 21, 55, 1343, 9892, 9892, 1343, 55, 144, 5734, 115110, 304889, 115110, 5734, 144, 377, 24495, 1339532, 9409503, 9409503, 1339532, 24495, 377, 987, 104655, 15587828, 290382196, 769212993, 290382196

Offset

1,4

Comments

Table starts

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

....1......17..........74.............315................1343

....3......74.........854............9892..............115110

....8.....315........9892..........304889.............9409503

...21....1343......115110.........9409503...........769212993

...55....5734.....1339532.......290382196.........62871566958

..144...24495....15587828......8961583206.......5138796600020

..377..104655...181392458....276566915938.....420019667031805

..987..447152..2110829288...8535237276423...34330314343879137

.2584.1910521.24563317752.263409237229182.2805988700231638418

Links

R. H. Hardin, Table of n, a(n) for n = 1..127

Formula

Empirical for column k:

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

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 21] for n>22

k=4: [order 80] for n>81

Example

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

Crossrefs

Column 1 is A001906(n-1)

Sequence in context: A174506 A109216 A090478 * A195421 A140446 A124689

Adjacent sequences: A231782 A231783 A231784 * A231786 A231787 A231788

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 13 2013

Status

approved