A049735 - OEIS

%I #14 Aug 07 2021 04:15:10

%S 1,5,5,13,9,13,29,21,21,29,49,37,25,37,49,81,57,45,45,57,81,113,89,69,

%T 61,69,89,113,149,121,97,81,81,97,121,149,197,161,129,109,101,109,129,

%U 161,197,253,213,177,145,137,137,145,177,213,253

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

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

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

%e Antidiagonals (each starting on row 0):

%e   {1},

%e   {5, 5},

%e   {13, 9, 13},

%e   ...

%e Array begins:

%e    1  5 13  29  49  81

%e    5  9 21  37  57  89

%e   13 21 25  45  69  97

%e   29 37 45  61  81 109

%e   49 57 69  81 101 137

%e   81 89 97 109 137 161

%o (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

%Y Cf. A000328 (1st column or row).

%K nonn,tabl

%O 0,2

%A _Clark Kimberling_