Riffs & Rotes

[Jon Awbrey]

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R&R.  Note 48

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A111798 [pending]

%I A111798
%S A111798 1 2 3 4 9 6 12 18 36
%N A111798 Positive integers sorted by rote height (A109301) and omega (A001221).
%C A111798 Positive integers m sorted by h(m) = A109301(m) and w(m) = A001221(m).
%C A111798 Defining the "wayage" of a rooted tree to be its root degree,
           the rote corresponding to the positive integer m has a wayage
           of w(m) = omega(m) = A001221(m).
%e A111798 Table of Integers, Primal Codes, Sort Parameters, and Subtotals
%e A111798 ` ` a ` code` ` | h w | s | t
%e A111798 ----------------+-----+---+---
%e A111798 ` ` 1 = { } ` ` | 0 0 | 1 | 1
%e A111798 ----------------+-----+---+---
%e A111798 ` ` 2 = 1:1 ` ` | 1 1 | 1 | 1
%e A111798 ----------------+-----+---+---
%e A111798 ` ` 3 = 2:1 ` ` | 2 1 | ` |
%e A111798 ` ` 4 = 1:2 ` ` | 2 1 | ` |
%e A111798 ` ` 9 = 2:2 ` ` | 2 1 | 3 |
%e A111798 ----------------+-----+---+---
%e A111798 ` ` 6 = 1:1 2:1 | 2 2 | ` |
%e A111798 ` `12 = 1:2 2:1 | 2 2 | ` |
%e A111798 ` `18 = 1:1 2:2 | 2 2 | ` |
%e A111798 ` `36 = 1:2 2:2 | 2 2 | 4 | 7
%e A111798 ----------------+-----+---+---
%e A111798 a = this sequence
%e A111798 h = rote height in gammas = A109301
%e A111798 w = rote wayage in gammas = A001221
%e A111798 s = count in (h, w) class = A111799
%e A111798 t = count in height class = A109300
%Y A111798 Cf. A001221, A061396, A062504, A062537, A062860.
%Y A111798 Cf. A109300, A109301, A111797, A111799, A111800.
%K A111798 nonn, tabf, new
%O A111798 1,2
%A A111798 Jon Awbrey (jawbrey(AT)att.net), Sep 01 2005

Incidental Musement:
Scots/English "weyage"/"wayage" --
http://www.dsl.ac.uk/getent4.php?dtext=all&query=Weyage

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