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A001604 Odd-indexed terms of A124297.
(Formerly M4785 N2042)
6

%I M4785 N2042

%S 11,31,151,911,5951,40051,272611,1863551,12760031,87424711,599129311,

%T 4106261531,28144128251,192901135711,1322159893351,9062207833151,

%U 62113268013311,425730597768451,2918000731816531,20000274041790911,137083916295800111,939587136717207031,6440026032054760351

%N Odd-indexed terms of A124297.

%C Old name: Related to factors of Fibonacci numbers.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H John Cerkan, <a href="/A001604/b001604.txt">Table of n, a(n) for n = 0..1187</a>

%H Dov Jarden, <a href="/A001602/a001602.pdf">Recurring Sequences</a>, Riveon Lematematika, Jerusalem, 1966. [Annotated scanned copy] See p. 20.

%H Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992.

%H Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">1031 Generating Functions and Conjectures</a>, Université du Québec à Montréal, 1992.

%F 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_]

%F 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]

%p 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

%t 5 #^2 + 5 # + 1 &@ Fibonacci@ # & /@ Range[1, 45, 2] (* _Michael De Vlieger_, Apr 03 2017 *)

%Y Cf. A001603, A124296, A124297.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_

%E Entry revised by _Michel Marcus_ and _N. J. A. Sloane_, Jun 06 2015

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Last modified December 13 22:53 EST 2019. Contains 329974 sequences. (Running on oeis4.)