cp's OEIS Frontend

A211339 Number of integer pairs (x,y) such that 1 < x <= y <= n and x^2 + y^2 <= n.

%I A211339 #13 Apr 07 2017 03:14:42
%S A211339 0,1,1,1,2,2,2,3,3,4,4,4,5,5,5,5,6,7,7,8,8,8,8,8,9,10,10,10,11,11,11,
%T A211339 12,12,13,13,13,14,14,14,15,16,16,16,16,17,17,17,17,17,19,19,20,21,21,
%U A211339 21,21,21,22,22,22,23,23,23,23,25,25,25,26,26,26,26,27,28,29
%N A211339 Number of integer pairs (x,y) such that 1 < x <= y <= n and x^2 + y^2 <= n.
%C A211339 Partial sums of A025426.
%C A211339 For a guide to related sequences, see A211266.
%F A211339 a(n) = -1/2(-1 + floor(sqrt(n/2)))(floor(sqrt(n/2))) + Sum_{k=1..floor(sqrt(n/2))} floor(sqrt(n - k^2)). - _Nicholas Stearns_, Apr 03 2017
%t A211339 a = 1; b = n; z1 = 120;
%t A211339 t[n_] := t[n] = Flatten[Table[x^2 + y^2, {x, a, b - 1}, {y, x, b}]]
%t A211339 c[n_, k_] := c[n, k] = Count[t[n], k]
%t A211339 TableForm[Table[c[n, k], {n, 1, 10}, {k, 1, 2 n}]]
%t A211339 Table[c[n, n], {n, 1, z1}]   (* A025426 *)
%t A211339 c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, a, m}]
%t A211339 Table[c1[n, n], {n, 1, z1}]  (* A211339 *)
%Y A211339 Cf. A211266.
%K A211339 nonn
%O A211339 1,5
%A A211339 _Clark Kimberling_, Apr 08 2012