A273968 T(n,k)=Number of nXk 0..3 arrays with no three equal values forming an isosceles triangle, and new values introduced in 0..3 order.

1, 2, 2, 5, 10, 5, 15, 105, 105, 15, 51, 1264, 1946, 1264, 51, 187, 13045, 24587, 24587, 13045, 187, 715, 136063, 211121, 49534, 211121, 136063, 715, 2795, 1273961, 2116450, 36817, 36817, 2116450, 1273961, 2795, 11051, 11936399, 15084593, 40569

Offset

1,2

Comments

Table starts

......1..........2..........5....15.....51.....187......715......2795.....11051

......2.........10........105..1264..13045..136063..1273961..11936399..95697853

......5........105.......1946.24587.211121.2116450.15084593.112714143.511843593

.....15.......1264......24587.49534..36817...40569....36570.....90627.....89429

.....51......13045.....211121.36817....356......10........0.........0

....187.....136063....2116450.40569.....10.......0........0

....715....1273961...15084593.36570......0.......0

...2795...11936399..112714143.90627......0

..11051...95697853..511843593.89429

..43947..800561388.2841058530

.175275.5824237329

.700075

Links

R. H. Hardin, Table of n, a(n) for n = 1..82

Formula

Empirical for column k:

k=1: a(n) = 7*a(n-1) -14*a(n-2) +8*a(n-3)

Example

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

Crossrefs

Column 1 is A007581(n-1).

Sequence in context: A193899 A334017 A208567 * A273964 A223062 A208788

Adjacent sequences: A273965 A273966 A273967 * A273969 A273970 A273971

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 05 2016

Status

approved