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A000036 Let A(n) = #{(i,j): i^2 + j^2 <= n}, V(n) = Pi*n, P(n) = A(n) - V(n); A000099 gives values of n where |P(n)| sets a new record; sequence gives closest integer to P(A000099(n)).

%I A000036 M0610 N0221 #26 Feb 03 2016 16:02:30
%S A000036 2,3,5,6,6,-6,7,8,10,13,13,13,14,-17,17,17,18,-19,20,-22,23,27,-29,
%T A000036 -29,29,-31,-32,-35,36,-37,-40,-43,-46,-48,-50,-53,-55,-57,-60,-60,
%U A000036 -61,-63,-66,-66,-68,-71,-74,-77,-79,-82,-85,-88,-89,-92,-95,-96,-97,-97,-100
%N A000036 Let A(n) = #{(i,j): i^2 + j^2 <= n}, V(n) = Pi*n, P(n) = A(n) - V(n); A000099 gives values of n where |P(n)| sets a new record; sequence gives closest integer to P(A000099(n)).
%D A000036 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000036 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000036 David W. Wilson, <a href="/A000036/b000036.txt">Table of n, a(n) for n = 1..200</a>
%H A000036 W. C. Mitchell, <a href="http://dx.doi.org/10.1090/S0025-5718-1966-0195834-3">The number of lattice points in a k-dimensional hypersphere</a>, Math. Comp., 20 (1966), 300-310.
%F A000036 a(n) = round(P(A000099(n))), where P(n) = A057655(n)-pi*n. - _David W. Wilson_, May 15 2008
%t A000036 nmax = 6*10^4; A[n_] := 1 + 4*Floor[Sqrt[n]] + 4*Floor[Sqrt[n/2]]^2 + 8* Sum[Floor[Sqrt[n - j^2]], {j, Floor[Sqrt[n/2]] + 1, Floor[Sqrt[n]]}]; V[n_] := Pi*n; P[n_] := A[n] - V[n]; record = 0; A000036 = Reap[For[k = 0; n = 1, n <= nmax, n++, p = Abs[pn = P[n]]; If[p > record, record = p; k++; Sow[pn // Round]; Print["a(", k, ") = ", pn // Round]]]][[2, 1]] (* _Jean-François Alcover_, Feb 03 2016 *)
%Y A000036 Cf. A000092, A000099, A000223, A000323, A000413.
%K A000036 sign
%O A000036 1,1
%A A000036 _N. J. A. Sloane_
%E A000036 Revised by _N. J. A. Sloane_, Jun 26 2005
%E A000036 More terms from _David W. Wilson_, May 15 2008