A231302 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with values 0..2 introduced in row major order

1, 2, 2, 4, 5, 4, 12, 16, 16, 12, 32, 51, 69, 51, 32, 92, 174, 301, 301, 174, 92, 264, 617, 1414, 1934, 1414, 617, 264, 756, 2223, 6850, 12150, 12150, 6850, 2223, 756, 2176, 8051, 33316, 78028, 103456, 78028, 33316, 8051, 2176, 6252, 29220, 162796, 503290

Offset

1,2

Comments

Table starts

....1......2.......4........12.........32...........92...........264

....2......5......16........51........174..........617..........2223

....4.....16......69.......301.......1414.........6850.........33316

...12.....51.....301......1934......12150........78028........503290

...32....174....1414.....12150.....103456.......894318.......7795257

...92....617....6850.....78028.....894318.....10359556.....122696560

..264...2223...33316....503290....7795257....122696560....1965819189

..756...8051..162796...3300161...68850102...1465475351...31830949407

.2176..29220..797293..21613114..608914401..17557687250..517419330480

.6252.106109.3906788.142211597.5409898598.211100299699.8451367403478

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

k=2: [order 8] for n>9

k=3: [order 14] for n>16

k=4: [order 44] for n>48

Example

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

Crossrefs

Sequence in context: A229402 A266249 A276299 * A231363 A225840 A361645

Adjacent sequences: A231299 A231300 A231301 * A231303 A231304 A231305

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 07 2013

Status

approved