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

0,2

Comments

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

Links

Table of n, a(n) for n=0..54.

Formula

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

Example

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

Prog

(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

Crossrefs

Cf. A000328 (1st column or row).

Sequence in context: A206553 A122213 A224067 * A055526 A146984 A055524

Adjacent sequences: A049732 A049733 A049734 * A049736 A049737 A049738

Keyword

nonn,tabl

Author

Clark Kimberling

Status

approved