[Inquiry] Re: Riffs & Rotes

[Jon Awbrey]

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R&R.  Note 68

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A113198 [pending]

%I A113198
%S A113198 1,1,2,2,4,2,2,8,8,1,8,12,4,4,28,16
%N A113198 Tetrahedron T(g, h, q) = number of rotes of weight g, height h, quench q.
%C A113198 T(g, h, q) = |{m : A062537(m) = g, A109301(m) = h, A108352(m) = q}|.
%C A113198 This is the column that is labeled "r" in the tabulation of A113197.
%e A113198 Table T(g, h, q), omitting empty cells, starts out as follows:
%e A113198 --------+------------------------------------------------------------
%e A113198 g\(h,q) | (0,1) ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
%e A113198 ` ` ` ` | ` ` ` (1,0) ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
%e A113198 ` ` ` ` | ` ` ` ` ` ` (2,0) (2,2) ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
%e A113198 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` (3,0) (3,2) (3,3) ` ` ` ` ` ` ` ` `
%e A113198 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` (4,0) (4,2) ` ` `
%e A113198 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` (5,2)
%e A113198 ========+============================================================
%e A113198 0 ` ` ` | ` 1 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
%e A113198 --------+------------------------------------------------------------
%e A113198 1 ` ` ` | ` ` ` ` 1 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
%e A113198 --------+------------------------------------------------------------
%e A113198 2 ` ` ` | ` ` ` ` ` ` ` ` ` ` 2 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
%e A113198 --------+------------------------------------------------------------
%e A113198 3 ` ` ` | ` ` ` ` ` ` ` 2 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
%e A113198 3 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 4 ` ` ` ` ` ` ` ` ` ` ` ` `
%e A113198 --------+------------------------------------------------------------
%e A113198 4 ` ` ` | ` ` ` ` ` ` ` 2 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
%e A113198 4 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` 2 ` ` 8 ` ` ` ` ` ` ` ` ` ` ` ` `
%e A113198 4 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 8 ` ` ` `
%e A113198 --------+------------------------------------------------------------
%e A113198 5 ` ` ` | ` ` ` ` ` ` ` 1 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
%e A113198 5 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` 8 ` `12 ` ` 4 ` ` ` ` ` ` ` ` ` `
%e A113198 5 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 4 ` `28 ` ` ` `
%e A113198 5 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `16 `
%e A113198 --------+------------------------------------------------------------
%e A113198 Row sums = A111793.  Horizontal section sums = A061396.
%Y A113198 Cf. A061396, A062504, A062537, A062860, A106177, A106178.
%Y A113198 Cf. A108352, A108353, A108370 to A108374, A109300, A109301.
%Y A113198 Cf. A111791 to A111801, A112846, A112868 to A112871, A113197.
%K A113198 nonn,tabf,new
%O A113198 1,3
%A A113198 Jon Awbrey (jawbrey(AT)att.net), Oct 18 2005

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