Riffs & Rotes

[Jon Awbrey]

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R&R.  Note 57

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A112096 [improved table]

%I A112096
%S A112096 1,1,2,1,1,4,2,8,2,8,1,12,12,28,4,16
%N A112096 Tetrahedron T(g, h, w) = number of rotes of weight g, height h, wayage w.
%C A112096 T(g, h, w) = |{m : A062537(m) = g, A109301(m) = h, A001221(m) = w}|.
%C A112096 This is the column that is labeled "r" in the tabulation of A112095.
%C A112096 g = h > 0 implies w = 1, and T(j, j, 1) = 2^(j-1) = A000079(j-1).
%e A112096 Table T(g, h, w), omitting empty cells, starts out as follows:
%e A112096 g\(h,w) | (0,0) (1,1) (2,1) (2,2) (3,1) (3,2) (4,1) (4,2) (5,1)
%e A112096 --------+-------------------------------------------------------
%e A112096 0 ` ` ` | ` 1
%e A112096 1 ` ` ` | ` ` ` ` 1
%e A112096 2 ` ` ` | ` ` ` ` ` ` ` 2
%e A112096 3 ` ` ` | ` ` ` ` ` ` ` 1 ` ` 1 ` ` 4
%e A112096 4 ` ` ` | ` ` ` ` ` ` ` ` ` ` 2 ` ` 8 ` ` 2 ` ` 8
%e A112096 5 ` ` ` | ` ` ` ` ` ` ` ` ` ` 1 ` `12 ` `12 ` `24 ` ` 4 ` `16
%Y A112096 Cf. A000079, A001221, A007097, A014221, A050924.
%Y A112096 Cf. A061396, A062504, A062537, A062860, A106177.
%Y A112096 Cf. A109300, A109301, A111791 to A111800, A112095.
%K A112096 nonn, tabf, new
%O A112096 1,3
%A A112096 Jon Awbrey (jawbrey(AT)att.net), Sep 08 2005, revised Sep 27 2005

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