

A133193


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.


0



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
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OFFSET

1,2


COMMENTS

The relative geometry is 5 to 1: 5 quarters to one dime in relative sizes. The counter geometry is seven dimes to one quarter.


LINKS

Table of n, a(n) for n=1..95.


FORMULA

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};


MATHEMATICA

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]


CROSSREFS

Cf. A131213.
Sequence in context: A137128 A256372 A133442 * A200131 A298907 A181909
Adjacent sequences: A133190 A133191 A133192 * A133194 A133195 A133196


KEYWORD

nonn,uned


AUTHOR

Roger L. Bagula, Oct 09 2007


STATUS

approved



