A274065 T(n,k)=Number of nXk 0..2 arrays with no three equal values forming an isosceles right triangle, and new values introduced in 0..2 order.

1, 2, 2, 5, 9, 5, 14, 50, 50, 14, 41, 285, 264, 285, 41, 122, 1617, 435, 435, 1617, 122, 365, 9188, 546, 8, 546, 9188, 365, 1094, 52193, 1209, 1, 1, 1209, 52193, 1094, 3281, 296511, 3272, 0, 0, 0, 3272, 296511, 3281, 9842, 1684466, 8412, 0, 0, 0, 0, 8412, 1684466, 9842

Offset

1,2

Comments

Table starts

.....1.......2.....5..14...41..122...365...1094....3281....9842.29525

.....2.......9....50.285.1617.9188.52193.296511.1684466.9569425

.....5......50...264.435..546.1209..3272...8412...20634

....14.....285...435...8....1....0.....0......0

....41....1617...546...1....0....0.....0

...122....9188..1209...0....0....0

...365...52193..3272...0....0

..1094..296511..8412...0

..3281.1684466.20634

..9842.9569425

.29525

Links

R. H. Hardin, Table of n, a(n) for n = 1..66

Formula

Empirical for column k:

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

k=2: a(n) = 6*a(n-1) -11*a(n-3) +4*a(n-4) for n>5

k=3: [order 40] for n>49

Example

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

Crossrefs

Column 1 is A007051(n-1).

Column 2 is A231413(n-1).

Sequence in context: A275401 A011273 A274068 * A233073 A275266 A223387

Adjacent sequences: A274062 A274063 A274064 * A274066 A274067 A274068

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 09 2016

Status

approved