A374276 - OEIS

%I #12 Jul 02 2024 10:19:44

%S 1,1,0,0,1,1,0,0,0,1,0,1,0,0,0,0,1,0,0,1,1,0,0,0,0,1,0,0,0,1,0,1,0,0,

%T 0,0,1,0,0,0,0,1,0,0,1,1,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,1,0,0,0,

%U 0,0,0,1,0,0,0,0,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,2

%N Number of representations of n by the quadratic form x^2 + 3*x*y + y^2 with 0 <= x <= y.

%F a(A031363(n)) > 0.

%e 121 = 0^2 + 3*0*11 + 11^2 = 3^2 + 3*3*7 + 7^2. So a(121) = 2.

%t a[n_]:=Module[{m=Floor[Sqrt[n]]},Sum[Sum[Boole[i^2+3i*j+j^2==n],{j,i,m}],{i,0,m}]]; Array[a,122,0] (* _Stefano Spezia_, Jul 02 2024 *)

%o (PARI) a(n) = my(m=sqrtint(n)); sum(i=0, m, sum(j=i, m, i^2+3*i*j+j^2==n));

%Y Cf. A031363, A088534, A374093, A374275.

%K nonn

%O 0,122

%A _Seiichi Manyama_, Jul 02 2024