Voozh

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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.

FORMULA

a(n) ~ A001622^(n+2) / n. - Vaclav Kotesovec, Oct 04 2025

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 *)

PROG

(Haskell)

a001461 n = a001461_list !! (n-1)

a001461_list = scanl1 (+) a006206_list -- Reinhard Zumkeller, Jun 01 2013

(SageMath)

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))

CROSSREFS

Sequence in context: A221942 A107368 A074733 * A048597 A332839 A319054

Adjacent sequences: A001458 A001459 A001460 * A001462 A001463 A001464