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

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

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)

a(n) ~ 7*n/16. - Charles R Greathouse IV, May 28 2026

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 *)

Prog

(PARI) a(n)=(n-1)\16*7+[7, 0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 6, 6, 7][n%16+1] \\ Charles R Greathouse IV, May 28 2026

Crossrefs

Cf. A194238.

Sequence in context: A269862 A194200 A242736 * A145707 A145703 A334231

Adjacent sequences: A194234 A194235 A194236 * A194238 A194239 A194240

Keyword

nonn,easy

Author

Clark Kimberling, Aug 20 2011

Status

approved