A194167 - OEIS

A194167

[sum{(k*r) : 1<=k<=n}], where [ ]=floor, ( )=fractional part, and r=(3+sqrt(5))/2, the golden ratio.

0, 0, 0, 1, 1, 2, 3, 4, 4, 4, 4, 5, 5, 6, 7, 8, 8, 8, 8, 8, 9, 9, 10, 11, 12, 12, 12, 12, 13, 13, 14, 15, 16, 16, 16, 16, 16, 17, 18, 18, 19, 20, 20, 20, 21, 21, 22, 22, 23, 24, 24, 24, 24, 25, 25, 26, 27, 27, 28, 29, 29, 29, 29, 30, 31, 31, 32, 32, 33, 33, 33, 34, 34, 35

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OFFSET

1,6

LINKS

Table of n, a(n) for n=1..74.

MATHEMATICA

r = 1/2 + GoldenRatio;

a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]

Table[a[n], {n, 1, 90}] (* A194167 *)

s[n_] := Sum[a[k], {k, 1, n}]

Table[s[n], {n, 1, 100}] (* A194168 *)

CROSSREFS