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A001604
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Odd-indexed terms of A124297.
(Formerly M4785 N2042)
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6
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11, 31, 151, 911, 5951, 40051, 272611, 1863551, 12760031, 87424711, 599129311, 4106261531, 28144128251, 192901135711, 1322159893351, 9062207833151, 62113268013311, 425730597768451, 2918000731816531, 20000274041790911, 137083916295800111, 939587136717207031, 6440026032054760351
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OFFSET
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0,1
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COMMENTS
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Old name: Related to factors of Fibonacci numbers.
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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John Cerkan, Table of n, a(n) for n = 0..1187
Dov Jarden, Recurring Sequences, Riveon Lematematika, Jerusalem, 1966. [Annotated scanned copy] See p. 20.
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
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FORMULA
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G.f.: -(11-90*x+173*x^2-90*x^3+11*x^4)/((x-1)*(x^2-3*x+1)*(x^2-7*x+1)). [After Simon Plouffe]
a(n) = (5+sqrt(5))/2*((3+sqrt(5))/2)^n+(5-sqrt(5))/2*((3-sqrt(5))/2)^n+(3+sqrt(5))/2*((7+3*sqrt(5))/2)^n+(3-sqrt(5))/2*((7-3*sqrt(5))/2)^n+3. [Tim Monahan, Aug 15 2011]
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MAPLE
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A001604:=-(11-90*z+173*z**2-90*z**3+11*z**4)/(z-1)/(z**2-3*z+1)/(z**2-7*z+1); # conjectured (correctly) by Simon Plouffe in his 1992 dissertation
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MATHEMATICA
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5 #^2 + 5 # + 1 &@ Fibonacci@ # & /@ Range[1, 45, 2] (* Michael De Vlieger, Apr 03 2017 *)
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CROSSREFS
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Cf. A001603, A124296, A124297.
Sequence in context: A094622 A193645 A190781 * A144727 A002535 A128337
Adjacent sequences: A001601 A001602 A001603 * A001605 A001606 A001607
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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Entry revised by Michel Marcus and N. J. A. Sloane, Jun 06 2015
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STATUS
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approved
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