A083656 a(n) = Sum_{i=1..n} floor(r*floor(r*i)), where r=sqrt(2).

1, 3, 8, 15, 24, 35, 47, 62, 78, 97, 118, 140, 165, 191, 220, 251, 284, 319, 355, 394, 435, 478, 523, 569, 618, 668, 721, 776, 833, 892, 952, 1015, 1080, 1147, 1216, 1286, 1359, 1433, 1510, 1589, 1669, 1752, 1836, 1923, 2012, 2103, 2196, 2290, 2387, 2485, 2586

Offset

1,2

Comments

Partial sums of A007069.

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Formula

a(n) = n*(n-1+1/sqrt(2)) + O(1).

Mathematica

Table[Sum[Floor[Sqrt[2]Floor[Sqrt[2]x]], {x, n}], {n, 60}] (* Harvey P. Dale, Jul 20 2018 *)

Prog

(PARI) a(n) = sum(i=1, n, floor(sqrt(2)*floor(sqrt(2)*i))); \\ Michel Marcus, Dec 05 2013
(Magma) [(&+[Floor(Sqrt(2)*Floor(Sqrt(2)*j)): j in [1..n]]): n in [1..60]]; // G. C. Greubel, Oct 01 2018

Crossrefs

Sequence in context: A191414 A086959 A335753 * A013648 A258837 A131386

Adjacent sequences: A083653 A083654 A083655 * A083657 A083658 A083659

Keyword

nonn

Author

Benoit Cloitre, Jun 13 2003

Status

approved