A194237 a(n) = [Sum_{k=1..n} (3k/8)], where [ ]=floor, ( )=fractional part.

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

Offset

1,5

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^12 + x^11 + x^9 + x^6 + x^4 + x)/(x^17 - x^16 - x + 1). (End)

Mathematica

r = 3/8;
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]    (* A194237 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194238 *)

Crossrefs

Cf. A194238.

Sequence in context: A269862 A194200 A242736 * A145707 A145703 A334231

Adjacent sequences: A194234 A194235 A194236 * A194238 A194239 A194240

Keyword

nonn

Author

Clark Kimberling, Aug 20 2011

Status

approved