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

0, 1, 3, 5, 9, 13, 17, 23, 30, 38, 45, 53, 64, 74, 86, 97, 110, 123, 138, 154, 168, 186, 203, 220, 241, 261, 282, 302, 324, 348, 370, 396, 421, 448, 476, 501, 531, 558, 591, 622, 651, 684, 717, 753, 788, 821, 858, 894, 933, 973, 1014, 1054, 1093, 1135

Offset

1,3

Comments

For a guide to related sequences, see A211266.

Links

Robert Israel, Table of n, a(n) for n = 1..2000

Maple

N:= 100: # for a(1)..a(N)
V:= Vector(N):
for y from 1 to N-1 do
  for x from 1 to y do
    r:= x^2 + y^2;
    if r > N^2 then break fi;
    t:= ceil(sqrt(r));
    V[t]:= V[t]+1
od od:
ListTools:-PartialSums(convert(V, list)); # Robert Israel, Jun 04 2019

Mathematica

a = 1; b = n; z1 = 120;
t[n_] := t[n] = Flatten[Table[x^2 + y^2, {x, a, b - 1}, {y, x, b}]] (* 1<=x<=y<=n *)
c[n_, k_] := c[n, k] = Count[t[n], k]
TableForm[Table[c[n, k], {n, 1, 7}, {k, 1, n^2}]]
Table[c[n, n^2], {n, 1, z1}]    (* A046080 *)
c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, a, m}]
Table[c1[n, n^2], {n, 1, z1/2}] (* A211340 *)

Crossrefs

Cf. A046080, A211266.

Sequence in context: A183859 A096228 A185170 * A061571 A049690 A080075

Adjacent sequences: A211337 A211338 A211339 * A211341 A211342 A211343

Keyword

nonn

Author

Clark Kimberling, Apr 08 2012

Status

approved