A130236 -id:A130236 - cp's OEIS frontend

A130262 Partial sums of the 'upper' even Fibonacci Inverse A130260.

0, 1, 3, 5, 8, 11, 14, 17, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 77, 82, 87, 92, 97, 102, 107, 112, 117, 122, 127, 132, 137, 142, 147, 152, 157, 162, 167, 172, 177, 182, 187, 192, 197, 202, 207, 212, 217, 222, 227, 232, 237, 242, 248, 254, 260, 266

Offset: 0

Hieronymus Fischer, May 25 2007

nonn

G. C. Greubel, Table of n, a(n) for n = 0..5000

Cf. A000045, A001519, A001906, A130234, A130235, A130236, A130256, A130259, A104161. Lucas inverse: A130241 - A130248.

[0] cat [(&+[ Ceiling(Log(Sqrt(5)*k)/(2*Log((1+ Sqrt(5))/2))): k in [1..n]]): n in [1..50]]; // G. C. Greubel, Sep 12 2018

Table[Sum[Ceiling[Log[GoldenRatio, Sqrt[5]*k]/2], {k, 1, n}], {n, 0, 60}] (* G. C. Greubel, Sep 12 2018 *)

for(n=0, 50, print1(sum(k=1,n, ceil(log(sqrt(5)*k)/(2*log((1+ sqrt(5))/2)))), ", ")) \\ G. C. Greubel, Sep 12 2018

a(n) = n*A130260(n) - A001519(A130260(n)) + 1.
a(n) = n*A130260(n) - Fib(2*A130260(n)-1) + 1.
G.f.: g(x)=x/(1-x)^2*Sum_{k>=0} x^Fib(2*k).

A130473 Partial sums of A087172.

Original entry on oeis.org

1, 3, 6, 9, 14, 19, 24, 32, 40, 48, 56, 64, 77, 90, 103, 116, 129, 142, 155, 168, 189, 210, 231, 252, 273, 294, 315, 336, 357, 378, 399, 420, 441, 475, 509, 543, 577, 611, 645, 679, 713, 747, 781, 815, 849, 883, 917, 951, 985, 1019, 1053, 1087, 1121, 1155, 1210

Offset: 1

Hieronymus Fischer, May 28 2007

nonn

Cf. A000045, A130233, A130234, A130235, A130236, A130238, A130240, A087172.

Accumulate[Flatten[Map[ConstantArray[Fibonacci[#],Fibonacci[#-1]]&,Range[15]]]] (* Peter J. C. Moses, May 02 2022 *)

a(n) = (1/2)*(Fib(2*b(n)+1) - 3*Fib(b(n))*Fib(b(n)+1)-1) + (n+1)*Fib(b(n)) where b(n) = A130233(n) = A130234(n+1)-1 and Fib(n)=A000045(n).

cp's OEIS Frontend

A130262 Partial sums of the 'upper' even Fibonacci Inverse A130260.

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