A273964 T(n,k)=Number of nXk 0..3 arrays with no three equal values forming an isosceles right triangle, and new values introduced in 0..3 order.

1, 2, 2, 5, 10, 5, 15, 105, 105, 15, 51, 1264, 2766, 1264, 51, 187, 15418, 49702, 49702, 15418, 187, 715, 188465, 784878, 543906, 784878, 188465, 715, 2795, 2304141, 13322548, 4010258, 4010258, 13322548, 2304141, 2795, 11051, 28171070, 232027264

Offset

1,2

Comments

Table starts

.........1.................2...................5............15......51......187

.........2................10.................105..........1264...15418...188465

.........5...............105................2766.........49702..784878.13322548

........15..............1264...............49702........543906.4010258.16365681

........51.............15418..............784878.......4010258.5029904...725420

.......187............188465............13322548......16365681..725420.....2890

.......715...........2304141...........232027264......55643290...30060.......12

......2795..........28171070..........4056338728.....210405148....1337........2

.....11051.........344428103.........70402715640.....904155053......54........0

.....43947........4211086174.......1221782263634....4384022592......11........0

....175275.......51486063258......21228810396872...21350702064.......0........0

....700075......629484802987.....368923543916728..105038486755.......0........0

...2798251.....7696279187803....6410003754557834..514302715276.......0

..11188907....94097130028610..111371494441358332.2558243582787

..44747435..1150461107685501.1935130749075453956

.178973355.14065899352150196

.715860651

Links

R. H. Hardin, Table of n, a(n) for n = 1..153

Formula

Empirical for column k:

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

k=2: [order 7] for n>8

Example

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

Crossrefs

Column 1 is A007581(n-1).

Sequence in context: A334017 A208567 A273968 * A223062 A208788 A246864

Adjacent sequences: A273961 A273962 A273963 * A273965 A273966 A273967

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 05 2016

Status

approved