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A124296
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5*F(n)^2 - 5*F(n) + 1, where F(n) = Fibonacci[n].
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6
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1, 1, 1, 11, 31, 101, 281, 781, 2101, 5611, 14851, 39161, 102961, 270281, 708761, 1857451, 4865911, 12744061, 33372361, 87382901, 228792301, 599019851, 1568309051, 4105974961, 10749725281, 28143378001, 73680695281, 192899171531
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| 11 = Lucas[5] divides a(3+10k), a(7+10k), a(8+10k). Last digit of a(n) is 1, or Mod[a(n),10] = 1. For odd n there exist so called Aurifeuillian factorization A001946[n] = Lucas[5n] = Lucas[n]*A[n]*B[n] = A000032[n]*A124296[n]*A124297[n], where A[n] = A124296[n] = 5*F(n)^2 - 5*F(n) + 1 and B[n] = A124297[n] = 5*F(n)^2 + 5*F(n) + 1, where F(n) = Fibonacci[n].
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FORMULA
| a(n) = 5*Fibonacci[n]^2 - 5*Fibonacci[n] + 1.
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MATHEMATICA
| Table[5*Fibonacci[n]^2-5*Fibonacci[n]+1, {n, 0, 50}]
5#^2-5#+1&/@Fibonacci[Range[0, 30]] (* From Harvey P. Dale, Nov 29 2011 *)
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CROSSREFS
| Cf. A000032, A000045, A121171, A001946, A124297.
Sequence in context: A027847 A068841 A192246 * A152220 A082712 A049090
Adjacent sequences: A124293 A124294 A124295 * A124297 A124298 A124299
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KEYWORD
| nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 25 2006
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