Riffs & Rotes

[Jon Awbrey]

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R&R.  Note 56

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A112096 [pending]

%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 | T
%e A112096 ------+---
%e A112096 0 0 0 | 1
%e A112096 1 1 1 | 1
%e A112096 2 2 1 | 2
%e A112096 3 2 1 | 1
%e A112096 3 2 2 | 1
%e A112096 3 3 1 | 4
%e A112096 4 2 2 | 2
%e A112096 4 3 1 | 8
%e A112096 4 3 2 | 2
%e A112096 4 4 1 | 8
%e A112096 5 2 2 | 1
%e A112096 5 3 1 |12
%e A112096 5 3 2 |12
%e A112096 5 4 1 |28
%e A112096 5 4 2 | 4
%e A112096 5 5 1 |16
%Y A112096 Cf. A000079, A001221, A007097, A050924.
%Y A112096 Cf. A061396, A062504, A062537, A062860.
%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

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