A048149 - OEIS

%I #17 Jan 14 2020 08:27:25

%S 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 28,35,45,37,30,26,26,30,37,45,58,48,39,33,31,33,39,48,58,73,62,52,43,

%U 41,41,43,52,62,73,90,75,64,54,50,48,50,54,64,75,90

%N 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 Seen as a triangle:

%e [0]  1;

%e [1]  3,  3;

%e [2]  6,  4,  6;

%e [3] 11,  8,  8, 11;

%e [4] 17, 13,  9, 13, 17;

%e [5] 26, 19, 15, 15, 19, 26;

%e [6] 35, 28, 22, 20, 22, 28, 35;

%e [7] 45, 37, 30, 26, 26, 30, 37, 45;

%e [8] 58, 48, 39, 33, 31, 33, 39, 48, 58;

%e [9] 73, 62, 52, 43, 41, 41, 43, 52, 62, 73;

%p A048149 := proc(n, k) option remember; ## n = 0 .. infinity and k = 0 .. n

%p     local x, y, radius, nTotal;

%p     if n >= k then

%p         radius := floor(sqrt(n^2 + k^2));

%p         nTotal := 0;

%p         for x from 0 to radius do

%p             nTotal := nTotal + floor(sqrt(n^2 + k^2 - x^2)) + 1;

%p         end do;

%p         return nTotal;

%p     else

%p         return A048149(k, n);

%p     end if;

%p end proc: # _Yu-Sheng Chang_, Jan 14 2020

%t 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 Cf. A000603 (right diagonal).

%K nonn,tabl

%O 0,2

%A _Clark Kimberling_

%E a(55) corrected by _Jean-François Alcover_, Nov 26 2013

%E a(55) restored by _Yu-Sheng Chang_, Jan 14 2020