A234717 a(n) = floor(n/(exp(1/(2*n))-1)).

1, 7, 16, 30, 47, 69, 94, 124, 157, 195, 236, 282, 331, 385, 442, 504, 569, 639, 712, 790, 871, 957, 1046, 1140, 1237, 1339, 1444, 1554, 1667, 1785, 1906, 2032, 2161, 2295, 2432, 2574, 2719, 2869, 3022, 3180, 3341, 3507

Offset

1,2

Comments

Equations of this general form: (n/(exp(1/(r*n))-1)) have a fractional portion that converges to one or more rational fractions if r is rational. They have second differences that are nearly constant before the floor function, and repeat in patterns when calculated after the floor function.

The fractional portion of this equation (before the floor function) oscillates between two fractions that converge towards 1/24 and 13/24.

Second differences of a(n) = repeat{3,5}.

First differences of a(n) = A075123(n+3).

Partial sums of a(n) = A033951(n).

Links

Table of n, a(n) for n=1..42.

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Formula

From Ralf Stephan, Mar 28 2014: (Start)

a(n) = (1/4)*(8n^2 - 2n - 1 + (-1)^n).

G.f.: x*(2*x^2 + 5*x + 1)/((1-x^2)*(1-x)^2). (End)

a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4). - Wesley Ivan Hurt, Apr 01 2022

E.g.f.: (x*(4*x + 3)*cosh(x) + (4*x^2 + 3*x - 1)*sinh(x))/2. - Stefano Spezia, Nov 23 2023

Mathematica

Table[Floor[n/(Exp[1/(2 n)] - 1)], {n, 100}] (* Wesley Ivan Hurt, Apr 01 2022 *)

Crossrefs

Cf. A033951, A075123.

Sequence in context: A211784 A180724 A212866 * A364352 A140511 A286119

Adjacent sequences: A234714 A234715 A234716 * A234718 A234719 A234720

Keyword

nonn,easy

Author

Richard R. Forberg, Dec 29 2013

Status

approved