cp's OEIS Frontend

A001603 Odd-indexed terms of A124296.

%I A001603 M4801 N2051 #48 Jun 25 2023 02:37:26
%S A001603 1,11,101,781,5611,39161,270281,1857451,12744061,87382901,599019851,
%T A001603 4105974961,28143378001,192899171531,1322154751061,9062194370461,
%U A001603 62113232767531,425730505493801,2918000490238361,20000273409331051,137083914639998701,939587132382262661
%N A001603 Odd-indexed terms of A124296.
%C A001603 Old name: Related to factors of Fibonacci numbers.
%D A001603 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001603 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001603 John Cerkan, <a href="/A001603/b001603.txt">Table of n, a(n) for n = 0..1187</a>
%H A001603 Dov Jarden, <a href="/A001602/a001602.pdf">Recurring Sequences</a>, Riveon Lematematika, Jerusalem, 1966. [Annotated scanned copy] See p. 20.
%H A001603 Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H A001603 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H A001603 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (11, -33, 33, -11, 1).
%F A001603 G.f.: -(1+13*x^2+x^4)/((x-1)*(x^2-3*x+1)*(x^2-7*x+1)). [After _Simon Plouffe_]
%p A001603 A001603:=-(1+13*z**2+z**4)/(z-1)/(z**2-3*z+1)/(z**2-7*z+1); # conjectured (correctly) by _Simon Plouffe_ in his 1992 dissertation
%t A001603 5 #^2 - 5 # + 1 &@ Fibonacci@ # & /@ Range[1, 43, 2] (* _Michael De Vlieger_, Apr 03 2017 *)
%Y A001603 Cf. A001604, A124296, A124297.
%K A001603 nonn,easy
%O A001603 0,2
%A A001603 _N. J. A. Sloane_
%E A001603 Entry revised by _Michel Marcus_ and _N. J. A. Sloane_, Jun 06 2015