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Search: id:A081010
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| A081010 |
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Fibonacci(4n+1)+2, or Fibonacci(2n-1)*Lucas(2n+2). |
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+0
1
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| 3, 7, 36, 235, 1599, 10948, 75027, 514231, 3524580, 24157819, 165580143, 1134903172, 7778742051, 53316291175, 365435296164, 2504730781963, 17167680177567, 117669030460996, 806515533049395, 5527939700884759
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75
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FORMULA
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a(n) = 8a(n-1)-8a(n-2)+a(n-3)
a(n) = 2 + .5[A001906(n+1)]^2 + .5[A001519(n)]^2 - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Aug 15 2004
a(n)=2+(1/2)*{[(7/2)-(3/2)*sqrt(5)]^n+[(7/2)+(3/2)*sqrt(5)]^n}+(1/10)*sqrt(5)*{[(7/2)+(3/2)*sqrt(5)]^n -[(7/2)-(3/2)*sqrt(5)]^n}, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Dec 01 2008]
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MAPLE
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with(combinat) for n from 0 to 25 do printf(`%d, `, fibonacci(4*n+1)+2) od
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CROSSREFS
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Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers).
Sequence in context: A102917 A156465 A049366 this_sequence A100377 A167169 A049493
Adjacent sequences: A081007 A081008 A081009 this_sequence A081011 A081012 A081013
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KEYWORD
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nonn,easy
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AUTHOR
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R. K. Guy (rkg(AT)cpsc.ucalgary.ca), Mar 01, 2003
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EXTENSIONS
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More terms and Maple code from James A. Sellers (sellersj(AT)math.psu.edu), Mar 03, 2003
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