A194235 a(n) = [Sum_{k=1..n} (k/8)], where [ ]=floor, ( )=fractional part.

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

Offset

1,6

Links

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

Formula

From Chai Wah Wu, Jun 10 2020: (Start)

a(n) = a(n-1) + a(n-16) - a(n-17) for n > 17.

G.f.: x*(x^14 + x^13 + x^12 + x^10 + x^6 + x^5 + x^3)/(x^17 - x^16 - x + 1). (End)

Mathematica

r = 1/8;
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]    (* A194235 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194236 *)

Prog

(PARI) a(n) = floor(sum(k=1, n, frac(k/8))); \\ Michel Marcus, Nov 03 2017

Crossrefs

Cf. A194236.

Sequence in context: A189627 A194227 A194819 * A029120 A078428 A337634

Adjacent sequences: A194232 A194233 A194234 * A194236 A194237 A194238

Keyword

nonn

Author

Clark Kimberling, Aug 20 2011

Status

approved