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Search: id:A029826
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| A029826 |
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Inverse of Salem polynomial: 1/(x^10+x^9-x^7-x^6-x^5-x^4-x^3+x+1). |
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+0
3
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| 1, -1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 2, 1, 2, 3, 2, 4, 3, 5, 5, 6, 8, 8, 10, 12, 14, 16, 20, 22, 27, 31, 37, 44, 50, 61, 70, 83, 98, 115, 135, 159, 187, 220, 259, 304, 359, 420, 496, 583, 685, 807, 948, 1116, 1312, 1544
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OFFSET
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0,14
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COMMENT
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The root 1.1762808182599175065440703384740350... is the smallest known Salem number.
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REFERENCES
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Lewin, Structural Properties of Polylogarithms, AMS #37. p. 365, 1991.
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FORMULA
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a(n) = -a(n - 1) + a(n - 3) + a(n - 4) + a(n - 5) + a(n - 6) + a(n - 7) - a(n - 9) - a(n - 10). - Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 23 2008
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MATHEMATICA
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Clear[a, n] (*A125950 a(0) to a(9) = 1; a(n + 10) = -a(n + 9) + a(n + 7) + a(n + 6) + a(n + 5) + a(n + 4) + a(n + 3) - a(n + 1) - a(n). *) a[0] = 1; a[1] = -1; a[2] = 1; a[3] = 0; a[4] = 0; a[5] = 1; a[6] = 0; a[7] = 1; a[8] = 0; a[9] = 1; a[n_] := a[n] = -a[n - 1] + a[n - 3] + a[n - 4] + a[n - 5] + a[n - 6] + a[n - 7] - a[n - 9] - a[n - 10]; Table[a[n], {n, 0, 100}] - Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 23 2008
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CROSSREFS
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Cf. A125950.
Sequence in context: A112779 A029201 A071283 this_sequence A080845 A029166 A096920
Adjacent sequences: A029823 A029824 A029825 this_sequence A029827 A029828 A029829
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KEYWORD
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sign
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AUTHOR
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Simon Plouffe (simon.plouffe(AT)gmail.com)
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