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A000692 An approximation to population of x^2 + y^2.
(Formerly M2311 N0913)
0

%I M2311 N0913

%S 1,3,4,5,9,15,27,50,92,171,322,610,1161,2220,4260,8201,15828,30622,

%T 59362,115287,224260,436871,852161,1664196,3253531,6366973,12471056,

%U 24447507,47962236,94161474,184983976,363632192,715220838,1407510311

%N An approximation to population of x^2 + y^2.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H D. Hare, <a href="http://www.plouffe.fr/simon/constants/landau.txt">The constant c</a> [Dave Hare, May 21 1996].

%H D. Shanks, <a href="http://dx.doi.org/10.1090/S0025-5718-1964-0159174-9">The second-order term in the asymptotic expansion of B(x)</a>, Math. Comp., 18 (1964), 75-86.

%H <a href="/index/Qua#quadpop">Index entries for sequences related to populations of quadratic forms</a>.

%F a(n)=(b*2^n/sqrt(n*log(2)))*(1+c/(n*log(2))) where b=0.764223654... is the Landau-Ramanujan constant (A064533) and c=0.5819486593... is the second-order Landau-Ramanujan constant (A227158) given by c=(1/2)*(1-log(Pi*e^gamma/(2*L)))-(1/4)deriv(log(prod(1/(1-p^(-2*s)),p prime = 3(mod 4)),s=1) where L is the Lemniscate constant (A064853). - _Sean A. Irvine_, Feb 25 2011

%Y Cf. A000690, A064533.

%K nonn

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Sean A. Irvine_, Feb 24 2011

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Last modified October 15 13:01 EDT 2018. Contains 316236 sequences. (Running on oeis4.)