A194021 Number of ways to arrange 4 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.

0, 0, 1, 8, 26, 75, 182, 387, 756, 1382, 2379, 3915, 6198, 9486, 14110, 20475, 29054, 40437, 55309, 74466, 98850, 129548, 167784, 214986, 272758, 342900, 427453, 528698, 649148, 791631, 959254, 1155429, 1383930, 1648890, 1954791, 2306565

Offset

1,4

Comments

Column 4 of A194024.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-4) + 5*a(n-6) - 3*a(n-7) + 3*a(n-8) - 5*a(n-9) + 2*a(n-11) + 2*a(n-13) - 3*a(n-14) + a(n-15).

Empirical g.f.: x^3*(1 + 5*x + 4*x^2 + 13*x^3 + 11*x^4 + 7*x^5 + 6*x^6 + x^7) / ((1 - x)^7*(1 + x)^2*(1 + x^2)*(1 + x + x^2)^2). - Colin Barker, May 05 2018

Example

Some solutions for 5 X 5 X 5:
......1..........1..........1..........1..........0..........0..........0
.....0.0........0.0........1.0........0.0........1.1........1.1........0.1
....0.1.1......1.0.0......0.0.0......1.1.0......0.0.1......0.0.0......1.1.0
...0.0.0.0....0.1.0.1....0.1.0.0....0.0.0.0....0.0.0.0....0.1.1.0....0.0.1.0
..0.1.0.0.0..0.0.0.0.0..0.0.0.1.0..0.0.0.1.0..0.1.0.0.0..0.0.0.0.0..0.0.0.0.0

Crossrefs

Cf. A194024.

Sequence in context: A051669 A207101 A027004 * A245126 A278769 A357593

Adjacent sequences: A194018 A194019 A194020 * A194022 A194023 A194024

Keyword

nonn

Author

R. H. Hardin, Aug 12 2011

Status

approved