A274959 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-1,-1) (-2,0) or (0,-2) and new values introduced in order 0..2.

1, 2, 2, 3, 9, 3, 6, 24, 24, 6, 12, 72, 90, 72, 12, 24, 216, 384, 384, 216, 24, 48, 648, 1638, 2376, 1638, 648, 48, 96, 1944, 6936, 14406, 14406, 6936, 1944, 96, 192, 5832, 29370, 87780, 126540, 87780, 29370, 5832, 192, 384, 17496, 124416, 536406, 1119744

Offset

1,2

Comments

Table starts

...1.....2.......3.........6.........12...........24.............48

...2.....9......24........72........216..........648...........1944

...3....24......90.......384.......1638.........6936..........29370

...6....72.....384......2376......14406........87780.........536406

..12...216....1638.....14406.....126540......1119744........9902040

..24...648....6936.....87780....1119744.....14362920......183551766

..48..1944...29370....536406....9902040....183551766.....3403449396

..96..5832..124416...3278016...87416934...2348053596....63272648886

.192.17496..527046..20027574..772181640..30087735576..1177544081274

.384.52488.2232600.122367012.6822635046.385522530402.21902996126304

Links

R. H. Hardin, Table of n, a(n) for n = 1..240

Formula

Empirical for column k:

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

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

k=3: a(n) = 4*a(n-1) +4*a(n-3) +a(n-4) for n>5

k=4: [order 9] for n>11

k=5: [order 25] for n>28

k=6: [order 81] for n>83

Example

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

Crossrefs

Column 1 is A003945(n-2).

Sequence in context: A132812 A203371 A181206 * A143307 A278463 A276248

Adjacent sequences: A274956 A274957 A274958 * A274960 A274961 A274962

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 12 2016

Status

approved