OFFSET
1,1
COMMENTS
LINKS
Wikipedia, Integer triangle
FORMULA
Empirical g.f.: -x*(x^5-x^4-x^3-2*x^2-2*x-3) / ((x-1)^2*(x^4+x^3+x^2+x+1)).
EXAMPLE
7 appears in the sequence because there exists a primitive 60-degree triangle with sides 7, 37 and 40.
PROG
(PARI)
\\ Gives terms not exceeding amax
\\ e.g. pt60a(25) gives [3, 5, 7, 8, 9, 11, 13, 15, 16, 17, 19, 21, 23, 24, 25]
pt60a(amax) = {
s=[];
for(m=1, amax\2,
for(n=1, m-1,
if((m-n)%3!=0 && gcd(m, n)==1,
if(2*m*n+n*n<=amax, s=concat(s, 2*m*n+n*n));
if(m*m-n*n<=amax, s=concat(s, m*m-n*n))
)
)
);
vecsort(s, , 8)
}
CROSSREFS
KEYWORD
nonn
AUTHOR
Colin Barker, Oct 01 2013
STATUS
approved