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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.

%I A048149 #17 Jan 14 2020 08:27:25
%S A048149 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,
%T A048149 28,35,45,37,30,26,26,30,37,45,58,48,39,33,31,33,39,48,58,73,62,52,43,
%U A048149 41,41,43,52,62,73,90,75,64,54,50,48,50,54,64,75,90
%N 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.
%e A048149 Seen as a triangle:
%e A048149 [0]  1;
%e A048149 [1]  3,  3;
%e A048149 [2]  6,  4,  6;
%e A048149 [3] 11,  8,  8, 11;
%e A048149 [4] 17, 13,  9, 13, 17;
%e A048149 [5] 26, 19, 15, 15, 19, 26;
%e A048149 [6] 35, 28, 22, 20, 22, 28, 35;
%e A048149 [7] 45, 37, 30, 26, 26, 30, 37, 45;
%e A048149 [8] 58, 48, 39, 33, 31, 33, 39, 48, 58;
%e A048149 [9] 73, 62, 52, 43, 41, 41, 43, 52, 62, 73;
%p A048149 A048149 := proc(n, k) option remember; ## n = 0 .. infinity and k = 0 .. n
%p A048149     local x, y, radius, nTotal;
%p A048149     if n >= k then
%p A048149         radius := floor(sqrt(n^2 + k^2));
%p A048149         nTotal := 0;
%p A048149         for x from 0 to radius do
%p A048149             nTotal := nTotal + floor(sqrt(n^2 + k^2 - x^2)) + 1;
%p A048149         end do;
%p A048149         return nTotal;
%p A048149     else
%p A048149         return A048149(k, n);
%p A048149     end if;
%p A048149 end proc: # _Yu-Sheng Chang_, Jan 14 2020
%t A048149 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 *)
%Y A048149 Cf. A000603 (right diagonal).
%K A048149 nonn,tabl
%O A048149 0,2
%A A048149 _Clark Kimberling_
%E A048149 a(55) corrected by _Jean-François Alcover_, Nov 26 2013
%E A048149 a(55) restored by _Yu-Sheng Chang_, Jan 14 2020