A274068 T(n,k)=Number of nXk 0..2 arrays with no three equal values forming an isosceles triangle, and new values introduced in 0..2 order.

1, 2, 2, 5, 9, 5, 14, 50, 50, 14, 41, 285, 136, 285, 41, 122, 1129, 111, 111, 1129, 122, 365, 4791, 97, 0, 97, 4791, 365, 1094, 17219, 235, 0, 0, 235, 17219, 1094, 3281, 63640, 197, 0, 0, 0, 197, 63640, 3281, 9842, 182143, 389, 0, 0, 0, 0, 389, 182143, 9842, 29525

Offset

1,2

Comments

Table starts

......1........2...5..14...41..122...365..1094...3281...9842...29525...88574

......2........9..50.285.1129.4791.17219.63640.182143.598332.1622713.4807733

......5.......50.136.111...97..235...197...389....305....589.....447.....823

.....14......285.111...0....0....0.....0.....0......0......0.......0

.....41.....1129..97...0....0....0.....0.....0......0......0

....122.....4791.235...0....0....0.....0.....0......0

....365....17219.197...0....0....0.....0.....0

...1094....63640.389...0....0....0.....0

...3281...182143.305...0....0....0

...9842...598332.589...0....0

..29525..1622713.447...0

..88574..4807733.823

.265721.12097755

.797162

Links

R. H. Hardin, Table of n, a(n) for n = 1..108

Formula

Empirical for column k:

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

k=3: a(n) = a(n-1) +2*a(n-2) -2*a(n-3) -a(n-4) +a(n-5) for n>13

Example

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

Crossrefs

Column 1 is A007051(n-1).

Sequence in context: A275504 A275401 A011273 * A274065 A233073 A275266

Adjacent sequences: A274065 A274066 A274067 * A274069 A274070 A274071

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 09 2016

Status

approved