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Search: id:A133193
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| A133193 |
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Two filled pentagons connected in a substitution graph in analogy to the hexagonal close pack A131213: the object is a 12 tone musical substitution. Characteristic polynomial: 12 + 120 x + 448 x^2 + 700 x^3 + 165 x^4 - 696 x^5 - 490 x^6 + 216 x^7 + 195 x^8 - 20 x^9 - 26 x^10 + x^12. |
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+0
1
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| 1, 3, 6, 8, 1, 4, 6, 11, 1, 2, 3, 4, 5, 12, 1, 8, 11, 12, 1, 3, 6, 8, 3, 5, 6, 10, 1, 2, 3, 4, 5, 12, 3, 8, 10, 12, 2, 5, 6, 7, 1, 3, 6, 8, 2, 4, 6, 9, 3, 5, 6, 10, 1, 4, 6, 11, 6, 7, 8, 9, 10, 11, 1, 3, 6, 8, 1, 8, 11, 12, 3, 8, 10, 12, 6, 7, 8, 9, 10, 11, 1, 3, 6, 8, 1, 4, 6, 11, 1, 2, 3, 4, 5, 12, 1
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The relative geometry is 5 to 1: 5 quarters to one dime in relative sizes. The counter geometry is seven dimes to one quarter.
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FORMULA
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1-> {2, 5, 6, 7};
2-> {1, 3, 6, 8};
3-> {2, 4, 6, 9};
4-> {3, 5, 6, 10};
5-> {1, 4, 6, 11};
6-> {1, 2, 3, 4, 5, 12};
7-> {1, 8, 11, 12};
8-> {2, 7, 9, 12};
9-> {3, 8,10, 12};
10-> {4, 9, 11, 12};
11-> {5, 7, 10, 12};
12-> {6, 7, 8, 9, 10, 11};
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MATHEMATICA
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Clear[s] s[1] = {2, 5, 6, 7}; s[2] = {1, 3, 6, 8}; s[3] = {2, 4, 6, 9}; s[4] = {3, 5, 6, 10}; s[5] = {1, 4, 6, 11}; s[6] = {1, 2, 3, 4, 5, 12}; s[7] = {1, 8, 11, 12}; s[8] = {2, 7, 9, 12}; s[9] = {3, 8, 10, 12}; s[10] = {4, 9, 11, 12}; s[11] = {5, 7, 10, 12}; s[12] = {6, 7, 8, 9, 10, 11}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]]; aa = p[4]
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CROSSREFS
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Cf. A131213.
Sequence in context: A067697 A137128 A133442 this_sequence A011334 A108369 A010621
Adjacent sequences: A133190 A133191 A133192 this_sequence A133194 A133195 A133196
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Oct 09 2007
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