A194016 T(n,k) = number of ways to arrange k points on an n X n X n triangular grid so that it balances at its center.

1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 3, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 12, 17, 0, 1, 0, 0, 1, 12, 0, 37, 9, 0, 0, 0, 0, 12, 0, 0, 63, 0, 0, 0, 0, 0, 9, 136, 0, 315, 108, 0, 1, 0, 0, 0, 3, 0, 909, 1293, 0, 165, 18, 0, 0, 0, 0, 1, 0, 0, 4350, 0, 0, 252, 0, 0, 0, 0, 0, 1, 136, 0, 12336, 16602, 0, 2517

Offset

1,13

Comments

Table starts

.1..0....0.....0......0........0.........0..........0...........0............0

.0..0....1.....0......0........0.........0..........0...........0............0

.0..0....2.....0......0........1.........0..........0...........0............0

.1..3....9....12.....12.......12.........9..........3...........1............1

.0..0...17.....0......0......136.........0..........0.........136............0

.0..0...37.....0......0......909.........0..........0........4130............0

.1..9...63...315...1293.....4350.....12336......29940.......62514.......113112

.0..0..108.....0......0....16602.........0..........0......604546............0

.0..0..165.....0......0....53679.........0..........0.....4291625............0

.1.18..252..2517..21270...152553....941628....5077137....24185859....102709611

.0..0..358.....0......0...391425.........0..........0...113919241............0

.0..0..506.....0......0...923809.........0..........0...464544503............0

.1.30..684.11619.166374..2033619..21584661..201864600..1682475175..12614546671

.0..0..917.....0......0..4220293.........0..........0..5516378285............0

.0..0.1192.....0......0..8326008.........0..........0.16616546191............0

.1.45.1539.39174.847551.15719472.254139258.3634785048.46520940879.537868088934

Links

R. H. Hardin, Table of n, a(n) for n = 1..543

Example

Some solutions for n=4, k=5:
.....1........0........0........1........1........0........0........0
....0.0......0.1......1.1......0.0......0.1......1.1......1.1......1.0
...1.0.1....1.1.1....0.1.0....0.1.1....0.0.0....1.0.0....0.1.0....1.1.1
..0.1.1.0..0.1.0.0..0.1.1.0..1.0.1.0..1.1.0.1..0.1.0.1..1.0.0.1..0.0.1.0

Crossrefs

Column 3 is A083707(n-1).

Sequence in context: A347715 A356305 A292247 * A292256 A095750 A056966

Adjacent sequences: A194013 A194014 A194015 * A194017 A194018 A194019

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 11 2011

Status

approved