A131212 D_6 like six sided prism as a substitution on a graph: characteristic polynomial is: 144 x^4 - 232 x^6 + 105 x^8 - 18 x^10 + x^12.

2, 6, 7, 2, 4, 9, 2, 7, 9, 2, 6, 7, 4, 6, 11, 6, 7, 11, 2, 6, 7, 2, 7, 9, 6, 7, 11, 2, 6, 7, 2, 4, 9, 2, 7, 9, 2, 4, 9, 4, 6, 11, 4, 9, 11, 2, 4, 9, 2, 7, 9, 4, 9, 11, 2, 6, 7, 2, 4, 9, 2, 7, 9, 2, 6, 7, 2, 7, 9, 6, 7, 11, 2, 4, 9, 2, 7, 9, 4, 9, 11, 2, 6, 7, 2, 4, 9, 2, 7, 9, 2, 6, 7, 4, 6, 11, 6, 7, 11, 2, 6

Offset

1,1

Comments

Each vertex has three connections in analogy to three tone musical chords and there are twelve vertices in analogy to a 12 tone scale. The sequence that results seems to be limited by the starting configuration: no "12" shows up in the first 5 substitutions.

Links

Table of n, a(n) for n=1..101.

Formula

Substitution of the form for 3 for 12 types: a(m)={a(n),a(o),a(p)}

Example

If "1" is the Note "A", then the chord substitution is A->B, Eflat,E

Mathematica

Clear[s] s[1] = {2, 6, 7}; s[2] = {1, 3, 8}; s[3] = {2, 4, 9}; s[4] = {3, 5, 10}; s[5] = {4, 6, 11}; s[6] = {1, 5, 12}; s[7] = {1, 8, 12}; s[8] = {2, 7, 9}; s[9] = {3, 8, 10}; s[10] = {4, 9, 11}; s[11] = {5, 10, 12}; s[12] = {6, 7, 11}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]]; aa = p[5]

Crossrefs

Sequence in context: A257478 A243523 A011044 * A020771 A242113 A261804

Adjacent sequences: A131209 A131210 A131211 * A131213 A131214 A131215

Keyword

nonn,uned

Author

Roger L. Bagula, Sep 27 2007

Status

approved