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A124297
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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, 11, 11, 31, 61, 151, 361, 911, 2311, 5951, 15401, 40051, 104401, 272611, 712531, 1863551, 4875781, 12760031, 33398201, 87424711, 228859951, 599129311, 1568486161, 4106261531, 10750188961, 28144128251, 73681909211, 192901135711
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 11 = Lucas[5] divides a(1+10k), a(2+10k), a(9+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}]
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CROSSREFS
| Cf. A000032, A000045, A121171, A001946, A124296.
Sequence in context: A022345 A152082 A070849 * A172507 A089766 A077699
Adjacent sequences: A124294 A124295 A124296 * A124298 A124299 A124300
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KEYWORD
| nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 25 2006
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