A000690 Landau's approximation to population of x^2 + y^2 <= 2^n. (Formerly M0586 N0212)

1, 2, 3, 4, 7, 13, 24, 44, 83, 157, 297, 567, 1085, 2086, 4019, 7766, 15039, 29181, 56717, 110408, 215225, 420076, 820836, 1605587, 3143562, 6160098, 12080946, 23710229, 46565965, 91512121, 179947985, 354043613, 696935548, 1372589372

Offset

0,2

References

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

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

Links

Sean A. Irvine, Table of n, a(n) for n = 0..999

D. Shanks, The second-order term in the asymptotic expansion of B(x), Mathematics of Computation 18 (1964), pp. 75-86.

Index entries for sequences related to populations of quadratic forms

Formula

a(n) = round(b*2^n/sqrt(log(2^n))) where b=0.764223654... is the Landau-Ramanujan constant (A064533).

Crossrefs

Cf. A000050, A064533.

Sequence in context: A341531 A099779 A270440 * A049876 A049795 A329111

Adjacent sequences: A000687 A000688 A000689 * A000691 A000692 A000693

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Feb 23 2011

Name clarified by Seth A. Troisi, Apr 28 2022

Status

approved