A183143 [1/r]+[2/r]+...+[n/r], where r=sqrt(3) and []=floor.

0, 1, 2, 4, 6, 9, 13, 17, 22, 27, 33, 39, 46, 54, 62, 71, 80, 90, 100, 111, 123, 135, 148, 161, 175, 190, 205, 221, 237, 254, 271, 289, 308, 327, 347, 367, 388, 409, 431, 454, 477, 501, 525, 550, 575, 601, 628, 655, 683, 711, 740, 770, 800, 831

Offset

1,3

Comments

A183143 + A183144 = A000217 (the triangular numbers).

Links

Table of n, a(n) for n=1..54.

Formula

[1/r]+[2/r]+...+[n/r], where r=sqrt(3) and []=floor.

Maple

A183143 := proc(n)
    local r;
    r := sqrt(3) ;
    add( floor(i/r), i=1..n) ;
end proc:
seq( A183143(n), n=1..200) ; # R. J. Mathar, Aug 28 2025

Mathematica

Accumulate[Floor[Range[60]/Sqrt[3]]] (* Harvey P. Dale, Sep 10 2019 *)

Prog

(PARI) default(realprecision, 100); r=sqrt(3); for(n=1, 99, print1(sum(k=1, n, floor(k/r)), ", "))

Crossrefs

Cf. A183142, A183144, A183136.

Sequence in context: A194178 A194213 A194209 * A184977 A025705 A022792

Adjacent sequences: A183140 A183141 A183142 * A183144 A183145 A183146

Keyword

nonn

Author

Clark Kimberling, Dec 26 2010

Status

approved