

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.


10



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
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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



