|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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).
|
|
LINKS
|
|
|
FORMULA
|
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)
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
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|