A113200 Tetrahedron T(g, q, h) = number of rotes of weight g, quench q, height h.

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

Offset: 1

Author

Jon Awbrey, Oct 18 2005

Keywords

• nonn
• tabf

Comments

T(g, q, h) = |{m : A062537(m) = g, A108352(m) = q, A109301(m) = h}|.

This is the column that is labeled "r" in the tabulation of A113199.

a(n) is a permutation of the elements in A113198.

Examples

			Table T(g, q, h), omitting empty cells, starts out as follows:
--------+------------------------------------------------------------
g\(q,h) | (1,0) (0,1) (0,2) ` ` ` (0,3) ` ` ` ` ` ` (0,4) ` ` ` ` ` `
` ` ` ` | ` ` ` ` ` ` ` ` ` (2,2) ` ` ` (2,3) ` ` ` ` ` ` (2,4) (2,5)
` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` (3,3) ` ` ` ` ` ` ` ` `
========+============================================================
0 ` ` ` | ` 1 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
--------+------------------------------------------------------------
1 ` ` ` | ` ` ` ` 1 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
--------+------------------------------------------------------------
2 ` ` ` | ` ` ` ` ` ` ` ` ` ` 2 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
--------+------------------------------------------------------------
3 ` ` ` | ` ` ` ` ` ` ` 2 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
3 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 4 ` ` ` ` ` ` ` ` ` ` ` ` `
--------+------------------------------------------------------------
4 ` ` ` | ` ` ` ` ` ` ` 2 ` ` ` ` ` 2 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
4 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 8 ` ` ` ` ` ` ` ` 8 ` ` ` `
--------+------------------------------------------------------------
5 ` ` ` | ` ` ` ` ` ` ` 1 ` ` ` ` ` 8 ` ` ` ` ` ` ` ` 4 ` ` ` ` ` ` `
5 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `12 ` ` ` ` ` ` ` `28 ` `16 `
5 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 4 ` ` ` ` ` ` ` ` ` `
--------+------------------------------------------------------------
Row sums = A112869. Horizontal section sums = A061396.
		

Links

• J. Awbrey, Riffs and Rotes

Crossrefs

Cf. A061396, A062504, A062537, A062860, A106177, A106178.

Cf. A108352, A108353, A108370 to A108374, A109300, A109301.

Cf. A111791 to A111801, A112868 to A112871, A113197 to A113199.