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A234717
a(n) = floor(n/(exp(1/(2*n))-1)).
0
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).
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
Sequence in context: A211784 A180724 A212866 * A364352 A140511 A286119
KEYWORD
nonn,easy
AUTHOR
Richard R. Forberg, Dec 29 2013
STATUS
approved