A000690 Landau's approximation to population of x^2 + y^2 <= 2^n.

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

Author

N. J. A. Sloane

Keywords

• nonn

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

Crossrefs

Cf. A000050, A064533.

Formula

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

Extensions

More terms from Sean A. Irvine, Feb 23 2011

Name clarified by Seth A. Troisi, Apr 28 2022