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A130244 Partial sums of the 'upper' Lucas Inverse A130242. 9
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 (list; graph; refs; listen; history; text; internal format)
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 A182814

Adjacent sequences:  A130241 A130242 A130243 * A130245 A130246 A130247

KEYWORD

nonn

AUTHOR

Hieronymus Fischer, May 19 2007

STATUS

approved

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Last modified January 22 09:52 EST 2019. Contains 319363 sequences. (Running on oeis4.)