A248873 a(n) = floor(e^(n+1) - e^n).

1, 4, 12, 34, 93, 255, 693, 1884, 5122, 13923, 37847, 102880, 279658, 760190, 2066413, 5617093, 15268842, 41505016, 112822331, 306682894, 833650539, 2266097111, 6159890600, 16744318683, 45515777207, 123724710091, 336318631172, 914208823689, 2485077232852, 6755140284380

Offset: 0

Author

Danny Rorabaugh, Mar 04 2015

Keywords

• nonn
• easy

Comments

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

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

Links

• Danny Rorabaugh, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, e
• Eric Weisstein's World of Mathematics, Floor Function

Crossrefs

Cf. A000149, A001113, A064780, A068996.

Programs

Mathematica

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

PARI

vector(30, n, n--; floor(exp(n+1)-exp(n))) \\ Michel Marcus, Mar 06 2015

Formula

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