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Search: id:A085151
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| A085151 |
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Numbers generated by the Fibonacci polynomial x^4 + 3x^2 + 1. |
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+0
1
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| 5, 29, 109, 305, 701, 1405, 2549, 4289, 6805, 10301, 15005, 21169, 29069, 39005, 51301, 66305, 84389, 105949, 131405, 161201, 195805, 235709, 281429, 333505, 392501, 459005, 533629, 617009, 709805, 812701, 926405, 1051649, 1189189
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OFFSET
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1,1
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COMMENT
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Start with the Fibonacci polynomials of A011973 (see "examples"), and put in appropriate exponents, e.g. {1,1} = x^2 + 1, the generator of A002522; {1,2} = x^3 + 2x, the generator of A054602; and to get the next polynomial, multiply by x and add the previous polynomial, such that the generator for A085151 = x^4 + 3x^2 + 1 = (x)(x^3+2x) + (x^2+1).
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FORMULA
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1. x^4 + 3x^2 + 1 2. a(n) = n*A054602(n) + A002522(n) 3. a(n) = denominator of [n, n, n, n]; with numerator = A054602(n).
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EXAMPLE
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1. a(2) = f(2) of x^4 + 3x^2 + 1 = 29
2. a(2) = 29 = (2)A054602 + A002522(2) = (2)(12) + 5.
3. [2,2,2,2] = 12/29; a(2) = 29, & 12 = A054602(2). Thus [n,n,n,n] = A054602(n)/A085151(n).
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MATHEMATICA
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f[n_] := n^4 + 3n^2 + 1; Array[f, 33] - Robert G. Wilson v, rgwv(AT)rgwv.com, Aug 6 2006
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CROSSREFS
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Cf. A054602, A002522, A011973.
Sequence in context: A097344 A034700 A057721 this_sequence A119494 A000352 A034332
Adjacent sequences: A085148 A085149 A085150 this_sequence A085152 A085153 A085154
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 21 2003
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EXTENSIONS
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More terms from Robert G. Wilson v, rgwv(AT)rgwv.com, Aug 6 2006
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