A130244 Partial sums of the 'upper' Lucas Inverse A130242.

0, 0, 0, 2, 5, 9, 13, 17, 22, 27, 32, 37, 43, 49, 55, 61, 67, 73, 79, 86, 93, 100, 107, 114, 121, 128, 135, 142, 149, 156, 164, 172, 180, 188, 196, 204, 212, 220, 228, 236, 244, 252, 260, 268, 276, 284, 292, 300, 309, 318, 327, 336, 345, 354, 363, 372, 381, 390

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..2500

Formula

a(n) = Sum_{k=0..n} A130242(k).

a(n) = n*A130242(n) - A000032(A130242(n) +1) for n>=3.

G.f.: x/(1-x)^2*(2*x^2 + Sum{k>=2, x^Lucas(k)}).

Mathematica

Join[{0, 0}, Table[Sum[Ceiling[Log[GoldenRatio, k + 1/2]], {k, 0, n}], {n, 1, 50}]] (* G. C. Greubel, Sep 12 2018 *)

Prog

(PARI) for(n=-1, 50, print1(if(n==-1, 0, if(n==0, 0, sum(k=0, n, ceil(log(k + 1/2)/log((1+sqrt(5))/2))))), ", ")) \\ G. C. Greubel, Sep 12 2018
(Magma) [0, 0] cat [(&+[Ceiling(Log(k + 1/2)/Log((1+Sqrt(5))/2)) : k in [0..n]]): n in [1..50]]; // G. C. Greubel, Sep 12 2018

Crossrefs

Other related sequences: A000032, A130241, A130243, A130245, A130246, A130248, A130252, A130258, A130262. Fibonacci inverse see A130233 - A130240, A104162.

Sequence in context: A060636 A050877 A063203 * A161569 A263086 A353036

Adjacent sequences: A130241 A130242 A130243 * A130245 A130246 A130247

Keyword

nonn

Author

Hieronymus Fischer, May 19 2007

Status

approved