A231363 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with values 0..3 introduced in row major order

1, 2, 2, 4, 5, 4, 12, 16, 16, 12, 33, 51, 69, 51, 33, 102, 180, 314, 314, 180, 102, 329, 685, 1588, 2190, 1588, 685, 329, 1075, 2735, 8664, 15384, 15384, 8664, 2735, 1075, 3622, 11243, 48485, 115303, 151357, 115303, 48485, 11243, 3622, 12298, 47120, 278067

Offset

1,2

Comments

Table starts

.....1......2.......4........12..........33...........102............329

.....2......5......16........51.........180...........685...........2735

.....4.....16......69.......314........1588..........8664..........48485

....12.....51.....314......2190.......15384........115303.........875548

....33....180....1588.....15384......151357.......1570792.......16473680

...102....685....8664....115303.....1570792......22223936......323672993

...329...2735...48485....875548....16473680.....323672993.....6484084119

..1075..11243..278067...6891052...177642195....4805725804...132637022443

..3622..47120.1614600..54253511..1920518549...71571627525..2720040353857

.12298.199945.9457286.432215971.20952334810.1071735830464.56182108648915

Links

R. H. Hardin, Table of n, a(n) for n = 1..143

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1) +5*a(n-2) -5*a(n-3) -24*a(n-4) -2*a(n-5) +15*a(n-6) +9*a(n-7)

k=2: [order 13] for n>14

k=3: [order 29] for n>31

k=4: [order 79] for n>83

Example

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

Crossrefs

Sequence in context: A266249 A276299 A231302 * A225840 A361645 A319409

Adjacent sequences: A231360 A231361 A231362 * A231364 A231365 A231366

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 08 2013

Status

approved