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A211340 Number of integer pairs (x,y) such that 1 and x^2+y^2<=n^2.

%I A211340 #11 Jun 04 2019 13:05:28
%S A211340 0,1,3,5,9,13,17,23,30,38,45,53,64,74,86,97,110,123,138,154,168,186,
%T A211340 203,220,241,261,282,302,324,348,370,396,421,448,476,501,531,558,591,
%U A211340 622,651,684,717,753,788,821,858,894,933,973,1014,1054,1093,1135
%N A211340 Number of integer pairs (x,y) such that 1<x<=y<=n and x^2+y^2<=n^2.
%C A211340 For a guide to related sequences, see A211266.
%H A211340 Robert Israel, <a href="/A211340/b211340.txt">Table of n, a(n) for n = 1..2000</a>
%p A211340 N:= 100: # for a(1)..a(N)
%p A211340 V:= Vector(N):
%p A211340 for y from 1 to N-1 do
%p A211340   for x from 1 to y do
%p A211340     r:= x^2 + y^2;
%p A211340     if r > N^2 then break fi;
%p A211340     t:= ceil(sqrt(r));
%p A211340     V[t]:= V[t]+1
%p A211340 od od:
%p A211340 ListTools:-PartialSums(convert(V,list)); # _Robert Israel_, Jun 04 2019
%t A211340 a = 1; b = n; z1 = 120;
%t A211340 t[n_] := t[n] = Flatten[Table[x^2 + y^2, {x, a, b - 1}, {y, x, b}]] (* 1<=x<=y<=n *)
%t A211340 c[n_, k_] := c[n, k] = Count[t[n], k]
%t A211340 TableForm[Table[c[n, k], {n, 1, 7}, {k, 1, n^2}]]
%t A211340 Table[c[n, n^2], {n, 1, z1}]    (* A046080 *)
%t A211340 c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, a, m}]
%t A211340 Table[c1[n, n^2], {n, 1, z1/2}] (* A211340 *)
%Y A211340 Cf. A046080, A211266.
%K A211340 nonn
%O A211340 1,3
%A A211340 _Clark Kimberling_, Apr 08 2012