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From variance of Fibonacci search.
(Formerly M3880)
2

%I M3880 #30 Dec 20 2021 08:00:32

%S 0,0,0,1,5,18,52,134,318,713,1531,3180,6432,12732,24756,47417,89665,

%T 167694,310628,570562,1040226,1883953,3391799,6073848,10824096,

%U 19204536,33936456

%N From variance of Fibonacci search.

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

%H K. J. Overholt, <a href="http://dx.doi.org/10.1007/BF01933527">Efficiency of the Fibonacci search method</a>, Nordisk Tidskr. Informationsbehandling (BIT) 13 (1973), 92-96.

%H 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 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992

%F (Conjecture equivalent to Plouffe g.f.): a(n) = -3 - 2*A001629(n+2) - 3*A001629(n+1) + 2*A001628(n-1) + A020701(n+1). - _R. J. Mathar_, Dec 06 2010

%p A006479:=z**3*(1+z+z**2)/(z-1)/(z**2+z-1)**3; # conjectured by _Simon Plouffe_ in his 1992 dissertation

%Y Cf. A006478.

%K nonn,nice,more

%O 0,5

%A _N. J. A. Sloane_