A252861 T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with every consecutive three elements in every row, column, diagonal and antidiagonal having exactly two distinct values, and new values 0 upwards introduced in row major order

117, 279, 279, 684, 432, 684, 1719, 738, 738, 1719, 4383, 1296, 1197, 1296, 4383, 11286, 2502, 1962, 1962, 2502, 11286, 29241, 4986, 3582, 3582, 3582, 4986, 29241, 76059, 9936, 6795, 7002, 7002, 6795, 9936, 76059, 198324, 20052, 12762, 13590

Offset

1,1

Comments

Table starts

....117...279...684...1719...4383...11286...29241...76059...198324...517923

....279...432...738...1296...2502....4986....9936...20052....40770....82872

....684...738..1197...1962...3582....6795...12762...24552....47367....91440

...1719..1296..1962...3582...7002...13590...26766...52650...104796...207414

...4383..2502..3582...7002..14229...28728...58644..119727...245016...501462

..11286..4986..6795..13590..28728...60588..126306..266391...562293..1185867

..29241..9936.12762..26766..58644..126306..275598..596250..1300068..2826126

..76059.20052.24552..52650.119727..266391..596250.1334322..3002328..6731217

.198324.40770.47367.104796.245016..562293.1300068.3002328..6954849.16128072

.517923.82872.91440.207414.501462.1185867.2826126.6731217.16128072.38574297

Links

R. H. Hardin, Table of n, a(n) for n = 1..311

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) -3*a(n-2) -2*a(n-3) +a(n-4)

k=2: [order 9]

k=3: a(n) = 2*a(n-1) -a(n-5) +a(n-6) -2*a(n-7) +a(n-8) for n>10

k=4: [order 10] for n>12

k=5: [order 16] for n>18

k=6: [order 23] for n>26

k=7: [order 34] for n>36

Example

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

Crossrefs

Sequence in context: A304611 A304610 A298047 * A252854 A156884 A255022

Adjacent sequences: A252858 A252859 A252860 * A252862 A252863 A252864

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 23 2014

Status

approved