A231641 T(n,k)=Number of nXk 0..2 arrays with no element having a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions)

1, 1, 1, 3, 5, 3, 8, 25, 25, 8, 21, 124, 362, 124, 21, 55, 599, 5110, 5110, 599, 55, 144, 2907, 69671, 193596, 69671, 2907, 144, 377, 14098, 953726, 7176194, 7176194, 953726, 14098, 377, 987, 68345, 13036446, 266730604, 722149510, 266730604

Offset

1,4

Comments

Table starts

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

....1.......5..........25............124.............599.............2907

....3......25.........362...........5110...........69671...........953726

....8.....124........5110.........193596.........7176194........266730604

...21.....599.......69671........7176194.......722149510......72839521581

...55....2907......953726......266730604.....72839521581...19935360619245

..144...14098....13036446.....9902703284...7337927223290.5448852806527104

..377...68345...178192422...367678630271.739300928401336

..987..331411..2435768976.13651615789060

.2584.1606976.33294651915

Links

R. H. Hardin, Table of n, a(n) for n = 1..84

Formula

Empirical for column k:

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

k=2: a(n) = 7*a(n-1) -11*a(n-2) +4*a(n-3) -14*a(n-4) +48*a(n-5) -48*a(n-6) +16*a(n-7)

k=3: [order 38] for n>39

Example

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

Crossrefs

Column 1 is A001906(n-1)

Sequence in context: A328915 A100338 A094444 * A099446 A198827 A199668

Adjacent sequences: A231638 A231639 A231640 * A231642 A231643 A231644

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 12 2013

Status

approved