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Search: id:A107470
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| A107470 |
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Bombieri matrix self-similar doubling to 9 symbols in substitution. |
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+0
1
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| 1, 1, 1, 1, 3, 3, 7, 7, 9, 1, 1, 1, 1, 3, 3, 7, 7, 9, 1, 1, 1, 1, 3, 3, 7, 7, 9, 1, 1, 1, 1, 3, 3, 7, 7, 9, 2, 2, 8, 2, 2, 8, 4, 4, 6, 4, 4, 6, 5, 1, 1, 1, 1, 3, 3, 7, 7, 9, 1, 1, 1, 1, 3, 3, 7, 7, 9, 1, 1, 1, 1, 3, 3, 7, 7, 9, 1, 1, 1, 1, 3, 3, 7, 7, 9, 2, 2, 8, 2, 2, 8, 4, 4, 6, 4, 4, 6, 5, 1, 1, 1, 1, 3, 3, 7
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Characteristic polynomial is -x^9+4*x^8+10*x^10-21*x^6-21*x^5+35*x^4+7*x^3-12*x^2-x+1. Roots are ( eight real roots, three are duplicates): {{x -> -1.80194}, {x -> -1.80194}, { x -> -0.445042}, {x -> -0.445042}, {x -> 0.307979}, {x -> 0.643104}, { x -> 1.24698}, {x -> 1.24698}, {x -> 5.04892}}.
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FORMULA
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1-> {1, 1, 1, 1, 3, 3, 7, 7, 9}; 2-> {1, 1, 3, 3, 7, 9}; 3-> {2, 2, 8}; 4-> {1, 1, 3, 7, 7, 9}; 5-> {1, 3, 7, 9}; 6-> {2, 8}; 7-> {4, 4, 6}; 8-> {4, 6}; 9-> {5};
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EXAMPLE
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Matrix is:
{{4, 0, 2, 0, 0, 0, 2, 0, 1},
{2, 0, 2, 0, 0, 0, 1, 0, 1},
{0, 2, 0, 0, 0, 0, 0, 1, 0},
{2, 0, 1, 0, 0, 0, 2, 0, 1},
{1, 0, 1, 0, 0, 0, 1, 0, 1},
{0, 1, 0, 0, 0, 0, 0, 1, 0},
{0, 0, 0, 2, 0, 1, 0, 0, 0},
{0, 0, 0, 1, 0, 1, 0, 0, 0},
{0, 0, 0, 0, 1, 0, 0, 0, 0}}
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MATHEMATICA
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s[1] = {1, 1, 1, 1, 3, 3, 7, 7, 9}; s[2] = {1, 1, 3, 3, 7, 9}; s[3] = {2, 2, 8}; s[4] = {1, 1, 3, 7, 7, 9}; s[5] = {1, 3, 7, 9}; s[6] = {2, 8}; s[7] = {4, 4, 6}; s[8] = {4, 6}; s[9] = {5}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]] aa = p[3]
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CROSSREFS
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Sequence in context: A105670 A003817 A092474 this_sequence A071042 A128053 A063212
Adjacent sequences: A107467 A107468 A107469 this_sequence A107471 A107472 A107473
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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), May 27 2005
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