A194202 a(n) = [Sum_{k=1..n} (2k*e)], where [ ]=floor, ( )=fractional part.

0, 1, 1, 2, 2, 3, 3, 3, 4, 5, 5, 6, 6, 6, 7, 8, 8, 9, 9, 10, 10, 11, 11, 11, 12, 13, 14, 14, 14, 15, 15, 16, 16, 17, 18, 18, 18, 19, 19, 19, 20, 21, 21, 22, 22, 22, 23, 24, 24, 25, 25, 26, 26, 27, 27, 27, 28, 28, 29, 29, 30, 30, 31, 32, 32, 33, 33, 34, 34, 34, 35, 36, 37

Offset

1,4

Links

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

Mathematica

r = 2E;
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]  (* A194202 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}] (* A194203 *)
Floor[Accumulate[FractionalPart[2 Range[80]E]]] (* Harvey P. Dale, Aug 16 2021 *)

Prog

(PARI) a(n) = floor(sum(k=1, n, frac(2*exp(1)*k))); \\ Michel Marcus, Nov 12 2017

Crossrefs

Cf. A194203.

Sequence in context: A115384 A131411 A300068 * A261224 A125059 A369611

Adjacent sequences: A194199 A194200 A194201 * A194203 A194204 A194205

Keyword

nonn

Author

Clark Kimberling, Aug 19 2011

Status

approved