Riffs & Rotes

[Jon Awbrey]

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

R&R.  Note 63

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

A112869 [pending]

%I A112869
%S A112869 1,1,2,2,4,4,16,13,56,4
%N A112869 Triangle T(g, q) = number of rotes of weight g and primal code characteristic q.
%C A112869 T(g, q) = |{positive integers m : A062537(m) = g and A108352(m) = q}|.
%C A112869 This is the column that is labeled "s" in the tabulation of A112868.
%C A112869 Row sums = A061396.
%e A112869 Table T(g, q), omitting empty cells, begins as follows:
%e A112869 g\q| 0 ` 1 ` 2 ` 3 ` 4 ` 5
%e A112869 ---+-----------------------
%e A112869 `0 | ` ` 1 ` ` ` ` ` ` ` `
%e A112869 `1 | 1 ` ` ` ` ` ` ` ` ` `
%e A112869 `2 | ` ` ` ` 2 ` ` ` ` ` `
%e A112869 `3 | 2 ` ` ` 4 ` ` ` ` ` `
%e A112869 `4 | 4 ` ` `16 ` ` ` ` ` `
%e A112869 `5 |13 ` ` `56 ` 4 ` ` ` `
%Y A112869 Cf. A061396, A062504, A062537, A062860, A106177, A106178.
%Y A112869 Cf. A108352, A108353, A108370 to A108374, A111800, A111801.
%Y A112869 Cf. A112846, A112868.
%K A112869 nonn,tabf,new
%O A112869 1,3
%A A112869 Jon Awbrey (jawbrey(AT)att.net), Oct 13 2005

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