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Tetrahedron T(g, w, h) = number of rotes of weight g, wayage w, height h.
2

%I #6 Nov 23 2013 23:45:07

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

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

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

%C This is the column that is labeled "r" in the tabulation of A112480.

%C a(n) is a permutation of the elements in A112096.

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

%H J. Awbrey, <a href="https://oeis.org/wiki/Riffs_and_Rotes">Riffs and Rotes</a>

%e Table T(g, w, h), omitting empty cells, starts out as follows:

%e --------+-------------------------------------------------------

%e g\(w,h) | (0,0) (1,1) (1,2) ` ` ` (1,3) ` ` ` (1,4) ` ` ` (1,5)

%e ` ` ` ` | ` ` ` ` ` ` ` ` ` (2,2) ` ` ` (2,3) ` ` ` (2,4) ` ` `

%e ========+=======================================================

%e 0 ` ` ` | ` 1 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `

%e --------+-------------------------------------------------------

%e 1 ` ` ` | ` ` ` ` 1 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `

%e --------+-------------------------------------------------------

%e 2 ` ` ` | ` ` ` ` ` ` ` 2 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `

%e --------+-------------------------------------------------------

%e 3 ` ` ` | ` ` ` ` ` ` ` 1 ` ` ` ` ` 4 ` ` ` ` ` ` ` ` ` ` ` ` `

%e 3 ` ` ` | ` ` ` ` ` ` ` ` ` ` 1 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `

%e --------+-------------------------------------------------------

%e 4 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` 8 ` ` ` ` ` 8 ` ` ` ` ` ` `

%e 4 ` ` ` | ` ` ` ` ` ` ` ` ` ` 2 ` ` ` ` ` 2 ` ` ` ` ` ` ` ` ` `

%e --------+-------------------------------------------------------

%e 5 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` `12 ` ` ` ` `28 ` ` ` ` `16 `

%e 5 ` ` ` | ` ` ` ` ` ` ` ` ` ` 1 ` ` ` ` `12 ` ` ` ` ` 4 ` ` ` `

%e --------+-------------------------------------------------------

%e Row sums = A111797. Horizontal section sums = A061396.

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

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

%Y Cf. A109300, A109301, A111791 to A111800.

%Y Cf. A112095, A112096, A112480.

%K nonn,tabf

%O 1,3

%A _Jon Awbrey_, Sep 27 2005