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A085151
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Numbers generated by the Fibonacci polynomial x^4 + 3x^2 + 1.
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2
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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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COMMENTS
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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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LINKS
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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
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MATHEMATICA
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f[n_] := n^4 + 3n^2 + 1; Array[f, 33]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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