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A182614 Least k such that floor(k/r^n)=n, where r = golden ratio = (1+sqrt(5))/2. 2

%I #12 Jan 12 2023 20:11:09

%S 2,6,13,28,56,108,204,376,685,1230,2190,3864,6774,11802,20461,35312,

%T 60708,104004,177632,302540,513997,871266,1473818,2488368,4194026,

%U 7057518,11858509,19898116,33345680,55814940,93320820,155867104

%N Least k such that floor(k/r^n)=n, where r = golden ratio = (1+sqrt(5))/2.

%F Conjectures from _Chai Wah Wu_, Jan 12 2023: (Start)

%F a(n) = 2*a(n-1) + 2*a(n-2) - 4*a(n-3) - 2*a(n-4) + 2*a(n-5) + a(n-6) for n > 6.

%F G.f.: x*(-2*x^4 + 2*x^3 + 3*x^2 - 2*x - 2)/((x - 1)*(x + 1)*(x^2 + x - 1)^2). (End)

%Y Cf. A001622, A182613, A182615.

%K nonn

%O 1,1

%A _Clark Kimberling_, Nov 22 2010

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Last modified April 19 06:44 EDT 2024. Contains 371782 sequences. (Running on oeis4.)