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A005830 a(n) = floor(tau*a(n-1)) + a(n-2) where tau is the golden ratio. 1

%I #18 Mar 05 2020 03:46:15

%S 1,3,5,11,22,46,96,201,421,882,1848,3872,8113,16999,35617,74628,

%T 156367,327635,686491,1438400,3013871,6314945,13231666,27724230,

%U 58090412,121716491,255031831,534366661,1119655250

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

%H Harvey P. Dale, <a href="/A005830/b005830.txt">Table of n, a(n) for n = 0..1000</a>

%H Michael Albert, Vít Jelínek, Michal Opler, <a href="https://arxiv.org/abs/1912.07713">Two examples of Wilf-collapse</a>, arXiv:1912.07713 [math.CO], 2019.

%t RecurrenceTable[{a[0]==1,a[1]==3,a[n]==Floor[GoldenRatio*a[n-1]]+a[n-2]},a,{n,30}] (* _Harvey P. Dale_, Dec 05 2018 *)

%Y Cf. A001622 (tau).

%K nonn

%O 0,2

%A _N. J. A. Sloane_

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Last modified April 19 05:19 EDT 2024. Contains 371782 sequences. (Running on oeis4.)