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Search: id:A130691
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| A130691 |
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Vector Matrix Markov with count up characteristic Pisot polynomial: -1 - 2 x - 3 x^2 - x^3. |
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+0
1
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| 0, 0, 1, -3, 7, -16, 37, -86, 200, -465, 1081, -2513, 5842, -13581, 31572, -73396, 170625, -396655, 922111, -2143648, 4983377, -11584946, 26931732, -62608681, 145547525, -338356945, 786584466, -1828587033, 4250949112, -9882257736, 22973462017
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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The form of the characteristic polynomial is different than most Pisots as all the coefficients are the same sign. It has a paired Pisot Polynomial of : x^3-7*x^2-x-1 These come from study of two matrices: ( suggested by the major minimal Pisot tile modes) A1 = {{x, x^5}, {-1, 0}} A2 = {{x^2, x^3}, {-1, 0}} Table[y /. NSolve[{CharacteristicPolynomial[A1, y] == 0, CharacteristicPolynomial[A2, y] == 0}, {x, y}][[n]], {n, 1, 7}] gives the second polynomial. Table[x /. NSolve[{CharacteristicPolynomial[A1, y] == 0, CharacteristicPolynomial[A2, y] == 0}, {x, y}][[n]], {n, 1, 7}] gives the first.
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FORMULA
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M = {{0, 1, 0}, {0, 0, 1}, {-1, -2, -3}}; v(n)=M.v(n-1); a(n) = v(n)[[1]]
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MATHEMATICA
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M = {{0, 1, 0}, {0, 0, 1}, {-1, -2, -3}}; v[0] = {0, 0, 1}; v[n_] := v[n] = M.v[n - 1]; a = Table[v[n][[1]], {n, 0, 30}]
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CROSSREFS
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Cf. A107335.
Sequence in context: A078056 A124671 A123392 this_sequence A095263 A010912 A052967
Adjacent sequences: A130688 A130689 A130690 this_sequence A130692 A130693 A130694
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KEYWORD
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uned,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jul 01 2007
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EXTENSIONS
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Is this the same as A095263 and A010912? If so these entries should be merged. - njas, Jul 13 2007
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