Riffs & Rotes

[Jon Awbrey]

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R&R.  Note 59

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A112481 [pending]

Hey Antti, how about a program for displaying tetrahedral and cubic arrays!?

Jon Awbrey

%I A112481
%S A112481 1,1,2,1,4,1,8,8,2,2,12,28,16,1,12,4
%N A112481 Tetrahedron T(g, w, h) = number of rotes of weight g, wayage w, height h.
%C A112481 T(g, w, h) = |{m : A062537(m) = g, A001221(m) = w, A109301(m) = h}|.
%C A112481 This is the column that is labeled "r" in the tabulation of A112480.
%C A112481 a(n) is a permutation of the elements in A112096.
%C A112481 g = h > 0 implies w = 1, and T(j, 1, j) = 2^(j-1) = A000079(j-1).
%e A112481 Table T(g, w, h), omitting empty cells, starts out as follows:
%e A112481 --------+-------------------------------------------------------
%e A112481 g\(w,h) | (0,0) (1,1) (1,2) ` ` ` (1,3) ` ` ` (1,4) ` ` ` (1,5)
%e A112481 ` ` ` ` | ` ` ` ` ` ` ` ` ` (2,2) ` ` ` (2,3) ` ` ` (2,4) ` ` `
%e A112481 ========+=======================================================
%e A112481 0 ` ` ` | ` 1 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
%e A112481 --------+-------------------------------------------------------
%e A112481 1 ` ` ` | ` ` ` ` 1 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
%e A112481 --------+-------------------------------------------------------
%e A112481 2 ` ` ` | ` ` ` ` ` ` ` 2 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
%e A112481 --------+-------------------------------------------------------
%e A112481 3 ` ` ` | ` ` ` ` ` ` ` 1 ` ` ` ` ` 4 ` ` ` ` ` ` ` ` ` ` ` ` `
%e A112481 3 ` ` ` | ` ` ` ` ` ` ` ` ` ` 1 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
%e A112481 --------+-------------------------------------------------------
%e A112481 4 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` 8 ` ` ` ` ` 8 ` ` ` ` ` ` `
%e A112481 4 ` ` ` | ` ` ` ` ` ` ` ` ` ` 2 ` ` ` ` ` 2 ` ` ` ` ` ` ` ` ` `
%e A112481 --------+-------------------------------------------------------
%e A112481 5 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` `12 ` ` ` ` `28 ` ` ` ` `16 `
%e A112481 5 ` ` ` | ` ` ` ` ` ` ` ` ` ` 1 ` ` ` ` `12 ` ` ` ` ` 4 ` ` ` `
%e A112481 --------+-------------------------------------------------------
%e A112481 Row sums = A111797.  Horizontal section sums = A061396.
%Y A112481 Cf. A000079, A001221, A007097, A014221, A050924.
%Y A112481 Cf. A061396, A062504, A062537, A062860, A106177.
%Y A112481 Cf. A109300, A109301, A111791 to A111800.
%Y A112481 Cf. A112095, A112096, A112480.
%K A112481 nonn, tabf, new
%O A112481 1,3
%A A112481 Jon Awbrey (jawbrey(AT)att.net), Sep 27 2005

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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