A001461 Partial sums of A006206.

1, 2, 3, 4, 6, 8, 12, 17, 25, 36, 54, 79, 119, 177, 267, 402, 612, 928, 1420, 2170, 3334, 5125, 7911, 12216, 18926, 29346, 45610, 70960, 110610, 172577, 269685, 421830, 660648, 1035603, 1625123

Offset: 1

Author

N. J. A. Sloane, David Broadhurst

Keywords

• nonn
• nice
• easy

Links

• James Spahlinger, Table of n, a(n) for n = 1..1000
• D. J. Broadhurst, On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory, arXiv:hep-th/9604128, 1996.

Programs

Haskell

a001461 n = a001461_list !! (n-1)
a001461_list = scanl1 (+) a006206_list -- Reinhard Zumkeller, Jun 01 2013

Maple

b := proc(n) local sum; sum := 0; for d in divisors(n) do sum := sum + mobius(n/d)*(fibonacci(d+1)+fibonacci(d-1)) od; RETURN(sum/n); end; A001461 := proc(n) local i; add(b(i),i=1..n); end;

Mathematica

b[n_] := Sum[MoebiusMu[n/d] (Fibonacci[d + 1] + Fibonacci[d - 1]), {d, Divisors[n]}]/n; Accumulate[Table[b[n], {n, 35}]] (* Jean-François Alcover, Dec 02 2011 *)

Sage

def a(n):
    return sum((fibonacci(d + 1) + fibonacci(d - 1)) * moebius(n // d) for d in divisors(n)) // n
def b(n):
    return sum(a(i) for i in range(1, n + 1))