OFFSET
1,1
COMMENTS
The mounting error seems to be approximately A035949(n-3), n >= 4. - Alonso del Arte, Jul 28 2011
This conjecture is false, for correct approximation see the formula below. - Vaclav Kotesovec, Apr 03 2017
REFERENCES
John H. Conway and Richard K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 95.
LINKS
Dr. Math, Partitioning the Integers
Dr. Math, Partitioning an Integer
D. Rusin, Additive Partitions of Number
F. Ruskey, Generate Numerical Partitions
Eric Weisstein's World of Mathematics, Partition Function P
OEIS Wiki, Partition function
FORMULA
a(n) = round(exp(Pi*sqrt(2*n/3))/(4*n*sqrt(3))). - Alonso del Arte, May 21 2011
a(n) - A000041(n) ~ (1/Pi + Pi/72) * exp(sqrt(2*n/3)*Pi) / (4*sqrt(2)*n^(3/2)) * (1 - (9 + Pi^2/48)*Pi/((72 + Pi^2)*sqrt(6*n))). - Vaclav Kotesovec, Apr 03 2017
MAPLE
A050811:=n->round(exp(Pi*sqrt(2*n/3))/(4*n*sqrt(3))): seq(A050811(n), n=1..70); # Wesley Ivan Hurt, Sep 11 2015
MATHEMATICA
f[n_] := Round[ E^(Sqrt[2n/3] Pi)/(4Sqrt[3] n)]; Array[f, 45] (* Alonso del Arte, May 21 2011, corrected by Robert G. Wilson v, Sep 11 2015 *)
PROG
(UBASIC) input N:print round(#e^(pi(1)*sqrt(2*N/3))/(4*N*sqrt(3)))
(PARI) a(n)=round(exp(Pi*sqrt(2*n/3))/(4*n*sqrt(3))) \\ Charles R Greathouse IV, May 01 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Patrick De Geest, Oct 15 1999
EXTENSIONS
a(1) = 1 replaced by 2, a(2) = 2 replaced by 3. - Alonso del Arte, D. S. McNeil, Aug 07 2011
STATUS
approved