Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the 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_