A049735 Array T(i,j) is the number of lattice points (x,y) in circle with radius (0,0)-to-(i,j), read by antidiagonals.

1, 5, 5, 13, 9, 13, 29, 21, 21, 29, 49, 37, 25, 37, 49, 81, 57, 45, 45, 57, 81, 113, 89, 69, 61, 69, 89, 113, 149, 121, 97, 81, 81, 97, 121, 149, 197, 161, 129, 109, 101, 109, 129, 161, 197, 253, 213, 177, 145, 137, 137, 145, 177, 213, 253

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• tabl

Comments

Specifically, x^2 + y^2 <= i^2 + j^2.

Examples

			Antidiagonals (each starting on row 0):
  {1},
  {5, 5},
  {13, 9, 13},
  ...
Array begins:
   1  5 13  29  49  81
   5  9 21  37  57  89
  13 21 25  45  69  97
  29 37 45  61  81 109
  49 57 69  81 101 137
  81 89 97 109 137 161
		

Crossrefs

Cf. A000328 (1st column or row).

Programs

PARI

T(n, k) = my(z=norml2([n, k]), m=ceil(sqrt(2)*max(n,k))); sum(x=-m, m, sum(y=-m, m, norml2([x, y]) <= z)); \\ Michel Marcus, Aug 07 2021

Formula

T(n,0) = A000328(n).