|
Search: id:A106795
|
|
|
| A106795 |
|
3-symbol substitution that has a real root cubic characteristic polynomial: x^3+9*x^2-3*x-1. |
|
+0
1
|
|
| 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 2, 2, 3, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 3, 1, 1, 1, 2, 2
(list; graph; listen)
|
|
|
OFFSET
|
0,7
|
|
|
COMMENT
|
The study of real root cubic Pisots by E. Bombieri and C. Frougny is related to the Penrose aperiodic tiling types. Roots hare are:{{x -> -0.20473}, {x -> 0.565376}, {x -> 8.63935}}
|
|
REFERENCES
|
Pure Discrete Spectrum for One Dimensional Substitution Systems of Pisot Type, V. F. Sirvent and B. Solomyak, page 14
|
|
FORMULA
|
1->{1, 1, 1, 1, 1, 1, 2, 2, 3, 3}, 2->{2, 2, 3, 1, 1, 1, 1}, 3->{3, 1, 1, 1, 2, 2}
|
|
MATHEMATICA
|
s[1] = {1, 1, 1, 1, 1, 1, 2, 2, 2, 3}; s[2] = {2, 2, 3, 1, 1, 1, 1}; s[3] = {3, 1, 1, 1, 2, 2}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]] aa = p[2]
|
|
CROSSREFS
|
Cf. A106749.
Adjacent sequences: A106792 A106793 A106794 this_sequence A106796 A106797 A106798
Sequence in context: A004481 A004489 A112599 this_sequence A071455 A139465 A010244
|
|
KEYWORD
|
nonn,uned
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 17 2005
|
|
|
Search completed in 0.002 seconds
|
