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 A050811 Partition numbers rounded to nearest integer given by the Hardy-Ramanujan approximate formula. 2
 2, 3, 4, 6, 9, 13, 18, 26, 35, 48, 65, 87, 115, 152, 199, 258, 333, 427, 545, 692, 875, 1102, 1381, 1725, 2145, 2659, 3285, 4046, 4967, 6080, 7423, 9037, 10974, 13293, 16065, 19370, 23304, 27977, 33519, 40080, 47833, 56981, 67757, 80431, 95316 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A000041, A035949, A049575, A051143. Sequence in context: A219282 A098578 A303667 * A076968 A238430 A285484 Adjacent sequences:  A050808 A050809 A050810 * A050812 A050813 A050814 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

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Last modified January 18 23:05 EST 2019. Contains 319282 sequences. (Running on oeis4.)