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

Author

Michel Marcus, Jan 11 2022

Keywords

• nonn

Links

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

Crossrefs

Cf. A000045, A000201, A185381.

Programs

Mathematica

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

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

Formula

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