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%I #24 Jan 12 2023 20:10:49
%S 3,7,16,34,66,125,232,422,760,1352,2388,4185,7294,12644,21824,37518,
%T 64278,109781,186980,317666,538472,910868,1537896,2592049,4361786,
%U 7328960,12297712,20608762,34495530,57675437,96331168,160737950,267960664,446321504,742796604,1235255433
%N Greatest k such that floor(k/r^n)=n, where r = golden mean = (1+sqrt(5))/2.
%F For n>=3, a(n)=-1+A182614(n)+A000032(n), where A000032 is the sequence of Lucas numbers.
%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 > 8.
%F G.f.: x*(-x^7 - x^6 + 3*x^5 + 4*x^2 - x - 3)/((x - 1)*(x + 1)*(x^2 + x - 1)^2). (End)
%e The integers k satisfying floor(k/r^3)=3 are 13,14,15,16, so that a(3)=16.
%o (PARI) a(n) = floor(((1+sqrt(5))/2)^n*(n+1)) \\ _David A. Corneth_, May 07 2022
%Y Cf. A001622, A182614, A000032.
%K nonn
%O 1,1
%A _Clark Kimberling_, Nov 22 2010
%E a(23) corrected by _Andrey Zabolotskiy_, May 07 2022
%E More terms from _David A. Corneth_, May 07 2022
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