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A107470 Bombieri matrix self-similar doubling to 9 symbols in substitution. 0
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; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

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}}.

LINKS

Table of n, a(n) for n=0..104.

FORMULA

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};

EXAMPLE

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}}

MATHEMATICA

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]

CROSSREFS

Sequence in context: A003817 A092474 A225851 * A228325 A071042 A128053

Adjacent sequences:  A107467 A107468 A107469 * A107471 A107472 A107473

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, May 27 2005

STATUS

approved

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Last modified February 17 17:52 EST 2019. Contains 320222 sequences. (Running on oeis4.)