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 A001604 Odd-indexed terms of A124297. (Formerly M4785 N2042) 6
 11, 31, 151, 911, 5951, 40051, 272611, 1863551, 12760031, 87424711, 599129311, 4106261531, 28144128251, 192901135711, 1322159893351, 9062207833151, 62113268013311, 425730597768451, 2918000731816531, 20000274041790911, 137083916295800111, 939587136717207031, 6440026032054760351 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Old name: Related to factors of Fibonacci numbers. REFERENCES 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). LINKS 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; arXiv:0911.4975 [math.NT], 2009. Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992 Index entries for linear recurrences with constant coefficients, signature (11, -33, 33, -11, 1). FORMULA 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] MAPLE 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 MATHEMATICA 5 #^2 + 5 # + 1 &@ Fibonacci@ # & /@ Range[1, 45, 2] (* Michael De Vlieger, Apr 03 2017 *) CROSSREFS Cf. A001603, A124296, A124297. Sequence in context: A094622 A193645 A190781 * A144727 A002535 A128337 Adjacent sequences: A001601 A001602 A001603 * A001605 A001606 A001607 KEYWORD nonn,easy AUTHOR N. J. A. Sloane EXTENSIONS Entry revised by Michel Marcus and N. J. A. Sloane, Jun 06 2015 STATUS approved

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Last modified February 28 04:16 EST 2024. Contains 370379 sequences. (Running on oeis4.)