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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.
4
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Aug 12 2011
STATUS
approved