A083704 a(n)=sum(k=1,n,floor(r*floor(k/r))) where r=sqrt(3).

0, 0, 1, 2, 5, 8, 13, 19, 25, 33, 41, 51, 61, 73, 86, 99, 114, 129, 146, 163, 182, 202, 222, 244, 266, 290, 315, 340, 367, 394, 423, 452, 483, 515, 547, 581, 615, 651, 687, 725, 764, 803, 844, 885, 928, 971, 1016, 1062, 1108, 1156, 1204, 1254, 1305, 1356, 1409

Offset

0,4

Comments

More generally if r is irrational 1<r<2 then sum(k=1,n,floor(r*floor(k/r))) = n(n-3)/2 + ceiling(n/r)

Links

Table of n, a(n) for n=0..54.

Formula

a(n) = n(n-3)/2 + ceiling(n/sqrt(3))

Crossrefs

Sequence in context: A289751 A200274 A122221 * A111097 A027916 A054254

Adjacent sequences: A083701 A083702 A083703 * A083705 A083706 A083707

Keyword

nonn

Author

Benoit Cloitre, Jun 15 2003

Status

approved