A120615 a(n) = Sum_{k=0..n} floor(phi*floor(k/phi)) where phi = (1+sqrt(5))/2.

0, 1, 2, 5, 9, 13, 19, 25, 33, 42, 51, 62, 74, 86, 100, 114, 130, 147, 164, 183, 202, 223, 245, 267, 291, 316, 341, 368, 395, 424, 454, 484, 516, 549, 582, 617, 652, 689, 727, 765, 805, 845, 887, 930, 973, 1018, 1064, 1110, 1158, 1206, 1256, 1307, 1358, 1411

Offset: 1

Author

Benoit Cloitre, Jun 17 2006

Keywords

• nonn

Crossrefs

Cf. A001622, A120613, A120614, A134945.

Programs

Mathematica

Table[Sum[Floor[GoldenRatio*Floor[k/GoldenRatio]],{k,0,n}],{n,54}] (* or *) Table[n(n-3)/2+Ceiling[n/GoldenRatio],{n,54}] (* James C. McMahon, Oct 07 2024 *)

PARI

phi=(1+sqrt(5))/2;a(n)=n*(n-3)/2+ceil(n/phi)

Formula

a(n) = n*(n-3)/2 + ceiling(n/phi).