A112096 Tetrahedron T(g, h, w) = number of rotes of weight g, height h, wayage w.

1, 1, 2, 1, 1, 4, 2, 8, 2, 8, 1, 12, 12, 28, 4, 16

Offset: 1

Author

Jon Awbrey, Sep 08 2005, revised Sep 27 2005

Keywords

• nonn
• tabf

Comments

T(g, h, w) = |{m : A062537(m) = g, A109301(m) = h, A001221(m) = w}|.

This is the column that is labeled "r" in the tabulation of A112095.

g = h > 0 implies w = 1 and T(j, j, 1) = 2^(j-1) = A000079(j-1).

Examples

			Table T(g, h, w), omitting empty cells, starts out as follows:
g\(h,w) | (0,0) (1,1) (2,1) (2,2) (3,1) (3,2) (4,1) (4,2) (5,1)
--------+-------------------------------------------------------
0 ` ` ` | ` 1
1 ` ` ` | ` ` ` ` 1
2 ` ` ` | ` ` ` ` ` ` ` 2
3 ` ` ` | ` ` ` ` ` ` ` 1 ` ` 1 ` ` 4
4 ` ` ` | ` ` ` ` ` ` ` ` ` ` 2 ` ` 8 ` ` 2 ` ` 8
5 ` ` ` | ` ` ` ` ` ` ` ` ` ` 1 ` `12 ` `12 ` `28 ` ` 4 ` `16
		

Links

• J. Awbrey, Riffs and Rotes

Crossrefs

Cf. A000079, A001221, A007097, A014221, A050924.

Cf. A061396, A062504, A062537, A062860, A106177.

Cf. A109300, A109301, A111791 to A111800, A112095.