A184976 a(n) = [e]+[2*e]+...+[n*e], where []=floor.

2, 7, 15, 25, 38, 54, 73, 94, 118, 145, 174, 206, 241, 279, 319, 362, 408, 456, 507, 561, 618, 677, 739, 804, 871, 941, 1014, 1090, 1168, 1249, 1333, 1419, 1508, 1600, 1695, 1792, 1892, 1995, 2101, 2209, 2320, 2434, 2550, 2669, 2791, 2916, 3043, 3173, 3306, 3441, 3579, 3720

Offset

1,1

Comments

It is interesting to note that a(n)/n^2 converges to e/2 .

Links

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

Formula

Partial sums of A022843.

Example

a(3) = 15 because [2.71828...] + [2*2.71828...] + [3*2.71828...] = 2 + 5 + 8 = 15.

Maple

with(numtheory):Digits:=100:s:=0:e:=exp(1):for n from 1 to 100 do: s:=s+floor(n*e):printf(`%d,
  `, s):od:

Mathematica

Accumulate[Table[Floor[E n], {n, 60}]] (* Harvey P. Dale, Jan 14 2012 *)

Prog

(PARI) for(n=1, 50, print1(sum(k=1, n, floor(exp(1)*k)), ", ")) \\ G. C. Greubel, Jun 02 2017

Crossrefs

Cf. A001113 (e), A022843.

Sequence in context: A350043 A167543 A332495 * A194140 A029888 A194112

Adjacent sequences: A184973 A184974 A184975 * A184977 A184978 A184979

Keyword

nonn

Author

Michel Lagneau, Mar 27 2011

Status

approved