A194241 [sum{(rk) : 1<=k<=n}], where [ ]=floor, ( )=fractional part, and r=(1+sqrt(3))/2.

0, 1, 1, 1, 2, 2, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 8, 9, 9, 10, 10, 11, 11, 11, 12, 13, 13, 14, 15, 15, 16, 16, 16, 17, 17, 18, 19, 19, 20, 20, 20, 21, 21, 21, 22, 22, 23, 24, 24, 25, 25, 25, 26, 26, 27, 28, 28, 28, 29, 30, 30, 30, 31, 32, 32, 32, 33, 33, 34, 35, 35, 36

Offset

1,5

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

L:= [seq(frac(k*(1+sqrt(3))/2), k=1..100)]:
map(floor, ListTools:-PartialSums(L)); # Robert Israel, Nov 20 2017

Mathematica

r = (1+Sqrt[3])/2;
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]    (* A194241 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194242 *)

Crossrefs

Cf. A194242.

Sequence in context: A207291 A364443 A194175 * A089575 A227737 A194177

Adjacent sequences: A194238 A194239 A194240 * A194242 A194243 A194244

Keyword

nonn

Author

Clark Kimberling, Aug 20 2011

Status

approved