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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.
4
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jun 05 2016
STATUS
approved