[Inquiry] Re: Riffs & Rotes

[Jon Awbrey]

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R&R.  Note 71

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A113200 [pending]

%I A113200
%S A113200 1,1,2,2,4,2,2,8,8,1,8,4,12,28,16,4
%N A113200 Tetrahedron T(g, q, h) = number of rotes of weight g, quench q, height h.
%C A113200 T(g, q, h) = |{m : A062537(m) = g, A108352(m) = q, A109301(m) = h}|.
%C A113200 This is the column that is labeled "r" in the tabulation of A113199.
%C A113200 a(n) is a permutation of the elements in A113198.
%e A113200 Table T(g, q, h), omitting empty cells, starts out as follows:
%e A113200 --------+------------------------------------------------------------
%e A113200 g\(q,h) | (1,0) (0,1) (0,2) ` ` ` (0,3) ` ` ` ` ` ` (0,4) ` ` ` ` ` `
%e A113200 ` ` ` ` | ` ` ` ` ` ` ` ` ` (2,2) ` ` ` (2,3) ` ` ` ` ` ` (2,4) (2,5)
%e A113200 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` (3,3) ` ` ` ` ` ` ` ` `
%e A113200 ========+============================================================
%e A113200 0 ` ` ` | ` 1 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
%e A113200 --------+------------------------------------------------------------
%e A113200 1 ` ` ` | ` ` ` ` 1 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
%e A113200 --------+------------------------------------------------------------
%e A113200 2 ` ` ` | ` ` ` ` ` ` ` ` ` ` 2 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
%e A113200 --------+------------------------------------------------------------
%e A113200 3 ` ` ` | ` ` ` ` ` ` ` 2 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
%e A113200 3 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 4 ` ` ` ` ` ` ` ` ` ` ` ` `
%e A113200 --------+------------------------------------------------------------
%e A113200 4 ` ` ` | ` ` ` ` ` ` ` 2 ` ` ` ` ` 2 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
%e A113200 4 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 8 ` ` ` ` ` ` ` ` 8 ` ` ` `
%e A113200 --------+------------------------------------------------------------
%e A113200 5 ` ` ` | ` ` ` ` ` ` ` 1 ` ` ` ` ` 8 ` ` ` ` ` ` ` ` 4 ` ` ` ` ` ` `
%e A113200 5 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `12 ` ` ` ` ` ` ` `28 ` `16 `
%e A113200 5 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 4 ` ` ` ` ` ` ` ` ` `
%e A113200 --------+------------------------------------------------------------
%e A113200 Row sums = A112869.  Horizontal section sums = A061396.
%Y A113200 Cf. A061396, A062504, A062537, A062860, A106177, A106178.
%Y A113200 Cf. A108352, A108353, A108370 to A108374, A109300, A109301.
%Y A113200 Cf. A111791 to A111801, A112868 to A112871, A113197 to A113199.
%K A113200 nonn,tabf,new
%O A113200 1,3
%A A113200 Jon Awbrey (jawbrey(AT)att.net), Oct 18 2005

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