A130237 - OEIS

%I #22 Mar 18 2023 03:56:28

%S 0,2,6,12,16,25,30,35,48,54,60,66,72,91,98,105,112,119,126,133,140,

%T 168,176,184,192,200,208,216,224,232,240,248,256,264,306,315,324,333,

%U 342,351,360,369,378,387,396,405,414,423,432,441,450,459,468,477,486,550

%N The 'lower' Fibonacci Inverse A130233(n) multiplied by n.

%H G. C. Greubel, <a href="/A130237/b130237.txt">Table of n, a(n) for n = 0..5000</a>

%F a(n) = n*A130233(n).

%F a(n) = n*floor(arcsinh(sqrt(5)*n/2)/log(phi)).

%F G.f.: (1/(1-x))*Sum_{k>=1} (Fib(k) + x/(1-x))*x^Fib(k).

%t Table[n*Floor[Log[GoldenRatio, 3/2 +n*Sqrt[5]]], {n,0,70}] (* _G. C. Greubel_, Mar 18 2023 *)

%o (Magma) [n*Floor(Log(3/2 +n*Sqrt(5))/Log((1+Sqrt(5))/2)): n in [0..70]]; // _G. C. Greubel_, Mar 18 2023

%o (SageMath) [n*int(log(3/2 +n*sqrt(5), golden_ratio)) for n in range(71)] # _G. C. Greubel_, Mar 18 2023

%Y Partial sums: A130238.

%Y Cf. A000045, A130233, A130234, A130235, A130236, A130238, A130239, A130240, A130243, A130246, A130248, A130239, A130251, A130253, A130257, A130261.

%K nonn

%O 0,2

%A _Hieronymus Fischer_, May 17 2007