Riffs & Rotes

[Jon Awbrey]

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R&R.  Note 67

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A113197 [pending]

%I A113197
%S A113197 1,2,3,4,6,9,5,7,8,16,12,18,10,14,13,23,25,27,49,64,81,512,11,17,19,32,
%T A113197 53,128,256,65536,36,26,46,50,54,98,125,162,2401,15,21,37,61,169,343,
%U A113197 529,625,729,4096,19683,262144,20,24,28,48,22,34,38,106,29,41,43,83,97
%N A113197 Positive integers sorted by rote weight, rote height, and rote quench.
%C A113197 For positive integer m, the rote weight in gammas is g(m) = A062537(m),
           the rote height in gammas is h(m) = A109301(m), and the rote quench or
           primal code characteristic is q(m) = A108352(m).
%H A113197 Jon Awbrey, <a href="http://stderr.org/pipermail/inquiry/2005-October/003122.html">Table for Rote Weights 0 to 5</a>
%e A113197 Primal Functions, Primal Codes, Sort Parameters, and Subtotals
%e A113197 ================================================================
%e A113197 Primal Function | ` ` ` Primal Code ` = ` a | g h q | r | s | t
%e A113197 ================================================================
%e A113197 { } ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 1 | 0 0 1 | 1 | 1 | 1
%e A113197 ================================================================
%e A113197 1:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 2 | 1 1 0 | 1 | 1 | 1
%e A113197 ================================================================
%e A113197 2:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 3 | 2 2 2 | ` | ` |
%e A113197 1:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 4 | 2 2 2 | 2 | 2 | 2
%e A113197 ================================================================
%e A113197 1:1 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 6 | 3 2 0 | ` | ` |
%e A113197 2:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 9 | 3 2 0 | 2 | 2 |
%e A113197 ----------------+---------------------------+-------+---+---+---
%e A113197 3:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 5 | 3 3 2 | ` | ` |
%e A113197 4:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 7 | 3 3 2 | ` | ` |
%e A113197 1:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 8 | 3 3 2 | ` | ` |
%e A113197 1:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `16 | 3 3 2 | 4 | 4 | 6
%e A113197 ================================================================
%e A113197 1:2 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `12 | 4 2 0 | ` | ` |
%e A113197 1:1 2:2 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `18 | 4 2 0 | 2 | 2 |
%e A113197 ----------------+---------------------------+-------+---+---+---
%e A113197 1:1 3:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `10 | 4 3 0 | ` | ` |
%e A113197 1:1 4:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `14 | 4 3 0 | 2 | ` |
%e A113197 ----------------+---------------------------+-------+---+---+---
%e A113197 6:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `13 | 4 3 2 | ` | ` |
%e A113197 9:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `23 | 4 3 2 | ` | ` |
%e A113197 3:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `25 | 4 3 2 | ` | ` |
%e A113197 2:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `27 | 4 3 2 | ` | ` |
%e A113197 4:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `49 | 4 3 2 | ` | ` |
%e A113197 1:6 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `64 | 4 3 2 | ` | ` |
%e A113197 2:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `81 | 4 3 2 | ` | ` |
%e A113197 1:9 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 512 | 4 3 2 | 8 |10 |
%e A113197 ----------------+---------------------------+-------+---+---+---
%e A113197 5:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `11 | 4 4 2 | ` | ` |
%e A113197 7:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `17 | 4 4 2 | ` | ` |
%e A113197 8:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `19 | 4 4 2 | ` | ` |
%e A113197 1:5 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `32 | 4 4 2 | ` | ` |
%e A113197 16:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `53 | 4 4 2 | ` | ` |
%e A113197 1:7 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 128 | 4 4 2 | ` | ` |
%e A113197 1:8 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 256 | 4 4 2 | ` | ` |
%e A113197 1:16` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 65536 | 4 4 2 | 8 | 8 |20
%e A113197 ================================================================
%e A113197 a = this sequence
%e A113197 g = rote weight in gammas = A062537
%e A113197 h = rote height in gammas = A109301
%e A113197 q = primal code character = A108352
%e A113197 r = number in (g,h,q) set = A113198
%e A113197 s = count in (g, h) class = A111793
%e A113197 t = count in weight class = A061396
%Y A113197 Cf. A061396, A062504, A062537, A062860, A106177, A106178.
%Y A113197 Cf. A108352, A108353, A108370 to A108374, A109300, A109301.
%Y A113197 Cf. A111791 to A111801, A112846, A112868 to A112871, A113198.
%K A113197 nonn,tabf,new
%O A113197 1,2
%A A113197 Jon Awbrey (jawbrey(AT)att.net), Oct 18 2005

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