A374276 Number of representations of n by the quadratic form x^2 + 3*x*y + y^2 with 0 <= x <= y.

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, 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, 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

Offset

0,122

Links

Table of n, a(n) for n=0..121.

Formula

a(A031363(n)) > 0.

Example

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

Mathematica

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 *)

Prog

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

Crossrefs

Cf. A031363, A088534, A374093, A374275.

Sequence in context: A364420 A368006 A374061 * A037281 A143241 A308064

Adjacent sequences: A374273 A374274 A374275 * A374277 A374278 A374279

Keyword

nonn

Author

Seiichi Manyama, Jul 02 2024

Status

approved