A130248 Partial sums of the Lucas Inverse A130247.

1, 1, 3, 6, 9, 12, 16, 20, 24, 28, 33, 38, 43, 48, 53, 58, 63, 69, 75, 81, 87, 93, 99, 105, 111, 117, 123, 129, 136, 143, 150, 157, 164, 171, 178, 185, 192, 199, 206, 213, 220, 227, 234, 241, 248, 255, 263, 271, 279, 287, 295, 303, 311, 319, 327, 335, 343, 351

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Formula

a(n) = Sum_{k=1..n} A130247(k).

a(n) = 2+(n+1)*A130247(n)-A000032(A130247(n)+2) for n>=3.

G.f.: (x - x^2 + 2*x^3 + Sum_{k>=3} x^Lucas(k))/(1-x)^2.

Mathematica

Join[{1, 1}, Table[Sum[Floor[Log[GoldenRatio, k + 1/2]], {k, 1, n}], {n, 3, 50}]] (* G. C. Greubel, Dec 24 2017 *)

Prog

(Python)
def A130248(n):
    if n == 1: return 1
    a, b, c = 2, 1, 2
    while b <= n:
        c += n+1
        a, b = b, a+b
    return c-a-b # Chai Wah Wu, Sep 07 2025

Crossrefs

Cf. A000032, A130241, A130242, A130243, A130244, A130245, A130246, A130247, A130251, A130252, A130257, A130261.

Fibonacci inverse see A130233 - A130240, A104162.

Sequence in context: A084515 A084525 A211274 * A203302 A214050 A260706

Adjacent sequences: A130245 A130246 A130247 * A130249 A130250 A130251

Keyword

nonn

Author

Hieronymus Fischer, May 19 2007

Status

approved