A350678 Partial sums of A185381.

0, 1, 3, 6, 14, 35, 69, 158, 302, 679, 1666, 3263, 7444, 18390, 36101, 82469, 157494, 353912, 868141, 1700181, 3878490, 7403068, 16630533, 40788350, 79876519, 182210674, 450124970, 883619407, 2018522577, 3854834480, 8662361456, 21248630481, 41613641555, 94929932728, 234513795173

Offset

0,3

Links

Table of n, a(n) for n=0..34.

Martin Griffiths, The Zeckendorf Representation of a Beatty-Related Fibonacci Sum, Fibonacci Quart. 53 (2015), no. 3, 230-236.

Formula

a(n) = Sum_{k=1..n} A185381(k).

Mathematica

f[n_] := Fibonacci[Floor[GoldenRatio * n]]; Accumulate @ Array[f, 35, 0] (* Amiram Eldar, Jan 11 2022 *)

Prog

(PARI) B(n) = (n+sqrtint(5*n^2))\2; \\ A000201
f(n) = fibonacci(B(n)); \\ A185381
a(n) = sum(k=1, n, f(k));
(Python)
from math import isqrt
from sympy import fibonacci
def A350678(n): return sum(fibonacci((i+isqrt(5*i**2))//2) for i in range(n+1)) # Chai Wah Wu, Jan 11 2022

Crossrefs

Cf. A000045, A000201, A185381.

Sequence in context: A275873 A018017 A184785 * A332362 A196479 A147772

Adjacent sequences: A350675 A350676 A350677 * A350679 A350680 A350681

Keyword

nonn

Author

Michel Marcus, Jan 11 2022

Status

approved