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A085487
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a(n) = p^n + q^n, p = (1 + sqrt(21))/2, q = (1 - sqrt(21))/2.
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0
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1, 11, 16, 71, 151, 506, 1261, 3791, 10096, 29051, 79531, 224786, 622441, 1746371, 4858576, 13590431, 37883311, 105835466, 295252021, 824429351, 2300689456, 6422836211, 17926283491, 50040464546, 139671882001, 389874204731, 1088233614736
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| p + q = 1, p*q = -5, p - q = sqrt(21).
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REFERENCES
| Thomas Koshy, "Fibonacci and Lucas Numbers with Applications", Wiley, 2001, p. 471.
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FORMULA
| G.f.:(10*x^2+x)/(1-x-5*x^2)
a(n)=n*sum(k=1..n, (binomial(k,n-k)*1^(2*k-n)*(5)^(n-k))/k) [From Dmitry Kruchinin KruchininDm(AT)gmail.com, May 16 2011]
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EXAMPLE
| a(5) = 151 = p^5 + q^5, with p = 2.79128...; q = -1.79128...
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PROG
| (Sage): [lucas_number2(n, 1, -5) for n in xrange(1, 11)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 14 2009]
(Maxima)
a(n):=n*sum((binomial(k, n-k)*1^(2*k-n)*(5)^(n-k))/k, k, 1, n)
[From Dmitry Kruchinin KruchininDm(AT)gmail.com, May 16 2011]
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CROSSREFS
| Cf. A015440.
Sequence in context: A032221 A032146 A032051 * A166663 A032327 A032075
Adjacent sequences: A085484 A085485 A085486 * A085488 A085489 A085490
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 02 2003
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