A183136 a(n) = [1/r]+[2/r]+...+[n/r], where r = golden ratio = (1+sqrt(5))/2 and []=floor.

0, 1, 2, 4, 7, 10, 14, 18, 23, 29, 35, 42, 50, 58, 67, 76, 86, 97, 108, 120, 132, 145, 159, 173, 188, 204, 220, 237, 254, 272, 291, 310, 330, 351, 372, 394, 416, 439, 463, 487, 512, 537, 563, 590, 617, 645, 674, 703, 733, 763, 794, 826, 858

Offset

1,3

Comments

a(n) + A183137(n) = A000217(n) (the triangular numbers).

Links

Table of n, a(n) for n=1..53.

Hector Zenil, N. Kiani, J. Tegner, Low Algorithmic Complexity Entropy-deceiving Graphs, arXiv preprint arXiv:1608.05972 [cs.IT], 2016.

Formula

a(n) = [1/r]+[2/r]+...+[n/r], where r = golden ratio = (1+sqrt(5))/2 and []=floor.

Example

The terms [k/r] are given by A060143 (and A005206): 0,1,1,2,3,3,4,4,5,6,6,7,8,8,...

Prog

(PARI) default(realprecision, 100); r=(1+sqrt(5))/2; for(n=1, 99, print1(sum(k=1, n, floor(k/r)), ", "))

Crossrefs

Cf. A183137, A000217, A005206, A060143, A060144.

Sequence in context: A014616 A184674 A227353 * A144873 A120679 A145106

Adjacent sequences: A183133 A183134 A183135 * A183137 A183138 A183139

Keyword

nonn

Author

Clark Kimberling, Dec 26 2010

Status

approved