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A131212
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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.
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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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.
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FORMULA
| Substitution of the form for 3 for 12 types: a(m)={a(n),a(o),a(p)}
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EXAMPLE
| If "1" is the Note "A", then the chord subsitution is A->B, Eflat,E
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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]
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CROSSREFS
| Sequence in context: A130726 A158915 A011044 * A020771 A021378 A201891
Adjacent sequences: A131209 A131210 A131211 * A131213 A131214 A131215
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 27 2007
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