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A005834 a(n) = floor( tau*a(n-2) ) + a(n-1) where tau is the golden ratio. 2

%I

%S 0,2,2,5,8,16,28,53,98,183,341,637,1188,2218,4140,7728,14426,26930,

%T 50271,93844,175184,327026,610479,1139618,2127393,3971333,7413527,

%U 13839278,25834616,48227038,90028324

%N a(n) = floor( tau*a(n-2) ) + a(n-1) where tau is the golden ratio.

%H Vincenzo Librandi, <a href="/A005834/b005834.txt">Table of n, a(n) for n = 0..1000</a>

%H P. Flajolet et al., <a href="http://algo.inria.fr/flajolet/Publications/FlGrKiPrTi94.pdf">Mellin Transforms And Asymptotics: Digital Sums</a>, Theoret. Computer Sci. 23 (1994), 291-314.

%t a[n_] := a[n] = Floor[GoldenRatio*a[n-2]] + a[n-1]; a[0] = 0; a[1] = 2; a[2] = 2; a /@ Range[0, 30]

%t (* _Jean-Fran├žois Alcover_, Jun 30 2011 *)

%K nonn

%O 0,2

%A _N. J. A. Sloane_.

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Last modified July 13 16:22 EDT 2020. Contains 335688 sequences. (Running on oeis4.)