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Search: id:A108165
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| A108165 |
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Let beta = positive real root of x^3-x^2-x-1; b(n) = 1 + ceiling((n-1)*beta); c(n)=b(n)-b(n-1); a(n)=a(n-1)+c(n). |
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+0
1
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| 2, 5, 9, 12, 15, 19, 22, 26, 29, 32, 36, 39, 42, 46, 49, 53, 56, 59, 63, 66, 70, 73, 76, 80, 83, 86, 90, 93, 97, 100, 103, 107, 110, 114, 117, 120, 124, 127, 130, 134, 137, 141, 144, 147, 151, 154, 157, 161, 164, 168, 171, 174, 178, 181, 185, 188, 191, 195, 198, 201
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Tribonacci version of A001950 using beta, the positive real root of x^3-x^2-x-1, as the constant.
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MATHEMATICA
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NSolve[x^3 - x^2 - x - 1 = 0, x] beta = 1.8392867552141612 a[n_] = 1 + Ceiling[(n - 1)*beta^2] (* A007066-like*) aa = Table[a[n], {n, 1, 100}] (*A076662-like*) b = Table[a[n] - a[n - 1], {n, 2, Length[aa]}] F[1] = 2; F[n_] := F[n] = F[n - 1] + b[[n]] (* A000195-like*) c = Table[F[n], {n, 1, Length[b] - 1}]
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CROSSREFS
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Cf. A007066, A076662, A001950.
Sequence in context: A050904 A057471 A099434 this_sequence A063957 A047385 A086814
Adjacent sequences: A108162 A108163 A108164 this_sequence A108166 A108167 A108168
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 13 2005
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EXTENSIONS
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Partially edited by N. J. A. Sloane (njas(AT)research.att.com), May 04 2007
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