OFFSET

1,3

COMMENTS

An upper bound on the number of solutions appears to be 1.5*sqrt(n). - T. D. Noe, Jun 14 2006

a(n) is also the total number of distinct quadratic forms of discriminant -4n. A232551 counts only the primitive quadratic forms of discriminant -4n (those with all coefficients pairwise coprime) and A234287 includes those by which some prime can be represented (those with all coefficients pairwise coprime or coefficient of x^2 is prime or coefficient of y^2 is prime). This sequence includes all quadratic forms like 2x^2 + 2xy + 4y^2 and 2x^2 + 4y^2 which are non-primitive and those like 4x^2 + 2xy + 4y^2 and 4x^2 + 4xy + 4y^2 by which no prime can be represented (those with no restrictions). - V. Raman, Dec 24 2013

LINKS

EXAMPLE

a(12)=4 because of (0,1,12), (0,2,6), (0,3,4), (2,2,2).

a(20)=5 because of (0,1,20), (0,2,10), (0,4,5), (1,2,6), (2,2,4).

MATHEMATICA

Table[cnt=0; Do[z=(n-x*y)/(x+y); If[IntegerQ[z], cnt++ ], {x, 0, Sqrt[n/3]}, {y, Max[1, x], Sqrt[x^2+n]-x}]; cnt, {n, 100}] (* T. D. Noe, Jun 14 2006 *)

CROSSREFS

KEYWORD

easy,nonn

AUTHOR

Colin Mallows, Jan 31 2002

EXTENSIONS

Corrected, extended and edited by John W. Layman, Dec 03 2004

STATUS

approved