A000691 Ramanujan's approximation to population of x^2 + y^2 <= 2^n. (Formerly M0713 N0263)

1, 2, 3, 5, 9, 16, 29, 52, 94, 175, 327, 616, 1169, 2231, 4273, 8215, 15842, 30628, 59345, 115208, 224040, 436343, 850981, 1661663, 3248231, 6356076, 12448925, 24402959, 47873156, 93984236, 184632691, 362938014, 713852252, 1404817026

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

Table of n, a(n) for n=0..33.

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

Maple

Digits:=500;
K:=.764223653589220662990698731250092328116790541393409514721686673
7496146416587328588384015050131312337219372691207925926341874206467
8084323063315434629380531605171169636177508819961243824994277683469
0516235139218719620569053295644670419176349770659569905712938660289
3858998296105166296089099177929836072973697200640316985128636517347
3921065768550978681981674707359066921; a:=n->round(evalf(K*int(1/sqrt(ln(t)), t=1..2^n))); # Salvador Perez (pies314(AT)hotmail.com), May 08 2005

Crossrefs

K = A064533.

Other population sequences for x^2 + y^2: A000050, A000690, A000692.

Sequence in context: A006788 A054650 A022857 * A192804 A255071 A103285

Adjacent sequences: A000688 A000689 A000690 * A000692 A000693 A000694

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Salvador Perez (pies314(AT)hotmail.com), May 08 2005

Corrected by Sean A. Irvine, Feb 24 2011

Name clarified by Seth A. Troisi, May 23 2022

Status

approved