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A130258
Partial sums of the 'upper' odd Fibonacci Inverse A130256.
5
0, 0, 2, 5, 8, 11, 15, 19, 23, 27, 31, 35, 39, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 93, 98, 103, 108, 113, 118, 123, 128, 133, 138, 143, 148, 154, 160, 166, 172, 178, 184, 190, 196, 202, 208, 214, 220, 226, 232, 238, 244, 250, 256, 262, 268, 274, 280, 286, 292
OFFSET
0,3
LINKS
FORMULA
a(n) = n*A130256(n) - A001906(A130256(n) -1).
a(n) = n*A130256(n) - Fib(2*A130256(n)-2) - 1.
G.f.: g(x) = x/(1-x)^2*Sum_{k>=0} x^Fib(2*k-1).
MATHEMATICA
Table[Sum[Ceiling[1/2*(1 + Log[GoldenRatio, (Sqrt[5]*k - 1)])], {k, 2, n}], {n, 0, 50}] (* G. C. Greubel, Sep 13 2018 *)
PROG
(PARI) for(n=0, 50, print1(if(n==0, 0, if(n==1, 0, sum(k=2, n, ceil( (1/2)*(1 + log(sqrt(5)*k - 1)/log((1+sqrt(5))/2)))))), ", ")) \\ G. C. Greubel, Sep 13 2018
(Magma) [0, 0] cat [(&+[Ceiling((1/2)*(1 + Log(Sqrt(5)*k-1)/Log((1+Sqrt(5))/2))): k in [2..n]]): n in [2..50]]; // G. C. Greubel, Sep 13 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, May 24 2007
STATUS
approved