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

1,3

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).

Links

Table of n, a(n) for n=1..16.

J. Awbrey, Riffs and Rotes

Example

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

Crossrefs

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

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

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

Sequence in context: A157125 A335941 A157143 * A217874 A323182 A229118

Adjacent sequences: A112093 A112094 A112095 * A112097 A112098 A112099

Keyword

nonn,tabf

Author

Jon Awbrey, Sep 08 2005, revised Sep 27 2005

Status

approved