A194024 T(n,k) = number of ways to arrange k points on an n X n X n triangular grid on an isosceles triangle so that it balances at the midpoint of its central altitude.

1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 4, 0, 0, 0, 0, 8, 13, 0, 0, 0, 0, 0, 0, 26, 0, 8, 0, 0, 0, 0, 0, 40, 75, 0, 0, 1, 0, 0, 0, 0, 47, 0, 182, 0, 12, 0, 0, 0, 0, 0, 39, 0, 0, 387, 107, 0, 0, 0, 0, 0, 0, 21, 0, 1606, 0, 756, 0, 18, 0, 0, 0, 0, 0, 7, 560, 0, 0, 4247, 1382, 0, 0, 1, 0, 0

Offset

1,9

Comments

Table starts:

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

.0..0...0.....0.....0.......0.......0.........0.........0...........0

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

.0..0...0.....8.....0.......0.......0.........0.........0...........0

.1..4..13....26....40......47......39........21.........7...........1

.0..0...0....75.....0.......0.......0.......560.........0...........0

.0..8...0...182.....0....1606.......0......6425.........0.......11970

.0..0...0...387.....0.......0.......0.....47385.........0...........0

.1.12.107...756..4247...19750...77775....262382....764759.....1939038

.0..0...0..1382.....0.......0.......0...1180469.........0...........0

.0.18...0..2379.....0..141611.......0...4530030.........0....85972989

.0..0...0..3915.....0.......0.......0..15317274.........0...........0

.1.24.432..6198.72732..723299.6211053..46696163.310813712..1848236136

.0..0...0..9486.....0.......0.......0.130554918.........0...........0

.0.32...0.14110.....0.2915773.......0.339126948.........0.24650185783

.0..0...0.20475.....0.......0.......0.826821895.........0...........0

Links

R. H. Hardin, Table of n, a(n) for n = 1..480

Example

Some solutions for n=5, k=3, balancing at the midpoint of row 3:
......1..........0..........0..........0..........1..........0..........1
.....0.0........0.1........1.0........0.0........0.0........0.1........0.0
....0.1.0......0.1.0......1.0.0......1.1.1......0.0.1......0.0.1......1.0.0
...0.0.0.0....0.1.0.0....0.0.0.1....0.0.0.0....0.0.0.0....1.0.0.0....0.0.0.0
..0.0.1.0.0..0.0.0.0.0..0.0.0.0.0..0.0.0.0.0..0.1.0.0.0..0.0.0.0.0..0.0.0.1.0

Crossrefs

Sequence in context: A187097 A094428 A277148 * A082786 A101638 A321379

Adjacent sequences: A194021 A194022 A194023 * A194025 A194026 A194027

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 12 2011

Status

approved