A179180 Partial sums of A007895.

0, 1, 2, 3, 5, 6, 8, 10, 11, 13, 15, 17, 20, 21, 23, 25, 27, 30, 32, 35, 38, 39, 41, 43, 45, 48, 50, 53, 56, 58, 61, 64, 67, 71, 72, 74, 76, 78, 81, 83, 86, 89, 91, 94, 97, 100, 104, 106, 109, 112, 115, 119, 122, 126, 130, 131, 133, 135, 137, 140, 142, 145

Offset

0,3

Comments

Total number of summands in Zeckendorf representations of all the numbers 1,2,...,n (for n>0); see the conjecture at A214979. - Clark Kimberling, Oct 23 2012

Links

Clark Kimberling, Table of n, a(n) for n = 0..10000

Christian Ballot, On Zeckendorf and Base b Digit Sums, Fibonacci Quarterly, Vol. 51, No. 4 (2013), pp. 319-325.

Vaclav Kotesovec, Graph - the asymptotic ratio

Formula

a(n) ~ c * n * log(n), where c = (phi-1)/(sqrt(5)*log(phi)) = 0.574369... and phi is the golden ratio (A001622) (Ballot, 2013). - Amiram Eldar, Dec 09 2021

Example

For n = 6, a(n) = 1+1+1+2+1+2 = 8.

Mathematica

s = Reverse[Table[Fibonacci[n + 1], {n, 1, 70}]];
t2 = Map[Length[Select[Reap[FoldList[(Sow[Quotient[#1, #2]]; Mod[#1, #2]) &, #, s]][[2, 1]], # > 0 &]] &, Range[z]]; v[n_] := Sum[t2[[k]], {k, 1, n}];
v1 = Table[v[n], {n, 1, z}]
(* Peter J. C. Moses, Oct 18 2012 *)
DigitCount[Select[Range[0, 500], BitAnd[#, 2*#] == 0&], 2, 1] // Accumulate (* Jean-François Alcover, Jan 25 2018 *)

Crossrefs

Cf. A001622, A007895, A214979.

Sequence in context: A092979 A135260 A248560 * A085921 A005243 A117045

Adjacent sequences: A179177 A179178 A179179 * A179181 A179182 A179183

Keyword

nonn

Author

Walt Rorie-Baety, Jun 30 2010

Extensions

Corrected term a(17); the working list of the terms were not in order. Walt Rorie-Baety, Jun 30 2010

Extended by Clark Kimberling, Oct 23 2012

Status

approved