A000694 Related to population of numbers of form x^2 + y^2.

1, 2, 4, 6, 11, 19, 34, 63, 117, 218, 411, 780, 1487, 2849, 5477, 10562, 20419, 39563, 76805, 149360, 290896, 567321, 1107775, 2165487, 4237384, 8299283, 16268639, 31915437, 62656158, 123088460, 241958676, 475901501, 936544684

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Shanks' paper gives erroneous value a(16)=10555. - Sean A. Irvine, Feb 25 2011

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

• 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. A000691.

Programs

Maple

Digits:=500;
K:=.764223653589220662990698731250092328116790541393409514721686673
7496146416587328588384015050131312337219372691207925926341874206467
8084323063315434629380531605171169636177508819961243824994277683469
0516235139218719620569053295644670419176349770659569905712938660289
3858998296105166296089099177929836072973697200640316985128636517347
3921065768550978681981674707359066921;
a:=n->round(evalf((2/3)*K*int(1/sqrt(ln(t)), t=1..2^n)));
# Sean A. Irvine, Feb 25 2011

Extensions

More terms from Sean A. Irvine, Feb 24 2011