login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

a(n) = floor(e^(n+1) - e^n).
3

%I #23 Apr 26 2024 03:29:33

%S 1,4,12,34,93,255,693,1884,5122,13923,37847,102880,279658,760190,

%T 2066413,5617093,15268842,41505016,112822331,306682894,833650539,

%U 2266097111,6159890600,16744318683,45515777207,123724710091,336318631172,914208823689,2485077232852,6755140284380

%N a(n) = floor(e^(n+1) - e^n).

%C e^(n+1)-e^n-1 < a(n) <= A064780(n) <= a(n)+1 < e^(n+1)-e^n+1.

%C Lim_{n->infinity} a(n)/e^(n+1) = (e-1)/e. [Corrected by _Altug Alkan_, Apr 25 2018]

%H Danny Rorabaugh, <a href="/A248873/b248873.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/e.html">e</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FloorFunction.html">Floor Function</a>

%F a(n) = floor(e^(n+1)-e^n).

%t Floor[#[[2]]-#[[1]]]&/@Partition[E^Range[0,30],2,1] (* _Harvey P. Dale_, Jul 24 2018 *)

%o (PARI) vector(30, n, n--; floor(exp(n+1)-exp(n))) \\ _Michel Marcus_, Mar 06 2015

%Y Cf. A000149, A001113, A064780, A068996.

%K nonn,easy

%O 0,2

%A _Danny Rorabaugh_, Mar 04 2015