A048149 Array T read by diagonals: T(i,j) = number of pairs (h,k) with h^2+k^2 <= i^2+j^2, h>=0, k >= 0.

1, 3, 3, 6, 4, 6, 11, 8, 8, 11, 17, 13, 9, 13, 17, 26, 19, 15, 15, 19, 26, 35, 28, 22, 20, 22, 28, 35, 45, 37, 30, 26, 26, 30, 37, 45, 58, 48, 39, 33, 31, 33, 39, 48, 58, 73, 62, 52, 43, 41, 41, 43, 52, 62, 73, 90, 75, 64, 54, 50, 48, 50, 54, 64, 75, 90

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• tabl

Examples

			Seen as a triangle:
[0]  1;
[1]  3,  3;
[2]  6,  4,  6;
[3] 11,  8,  8, 11;
[4] 17, 13,  9, 13, 17;
[5] 26, 19, 15, 15, 19, 26;
[6] 35, 28, 22, 20, 22, 28, 35;
[7] 45, 37, 30, 26, 26, 30, 37, 45;
[8] 58, 48, 39, 33, 31, 33, 39, 48, 58;
[9] 73, 62, 52, 43, 41, 41, 43, 52, 62, 73;
		

Crossrefs

Cf. A000603 (right diagonal).

Programs

Maple

A048149 := proc(n, k) option remember; ## n = 0 .. infinity and k = 0 .. n
    local x, y, radius, nTotal;
    if n >= k then
        radius := floor(sqrt(n^2 + k^2));
        nTotal := 0;
        for x from 0 to radius do
            nTotal := nTotal + floor(sqrt(n^2 + k^2 - x^2)) + 1;
        end do;
        return nTotal;
    else
        return A048149(k, n);
    end if;
end proc: # Yu-Sheng Chang, Jan 14 2020

Mathematica

t[i_, j_] := Module[{h, k}, Reduce[h^2 + k^2 <= i^2 + j^2 && h >= 0 && k >= 0, {h, k}, Integers] // ToRules // Length[{##}]&]; Table[t[n-k, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Nov 26 2013 *)

Extensions

a(55) corrected by Jean-François Alcover, Nov 26 2013

a(55) restored by Yu-Sheng Chang, Jan 14 2020