OFFSET
1,1
LINKS
Artūras Dubickas, On the number of reducible polynomials of bounded naive height, manuscripta math. 144, 439-456 (2014).
Phyllis Lefton, On the Galois groups of cubics and trinomials, Bull. Amer. Math. Soc., vol. 82 (1976), pp. 754-756.
Phyllis Lefton, On the Galois groups of cubics and trinomials, Acta Arithmetica (1979) Volume: 35, Issue: 3, page 239-246.
FORMULA
Dubickas (2014) shows that a(n) ~ 2(1+(2/3)Pi^2)n^2 = 15.1598... n^2 for large n.
PROG
(PARI)
{ a(n) =
my( ct = 0 );
for (c1 = -n, n,
for (c2 = -n, n,
for (c3 = -n, n,
if ( ! polisirreducible( Pol([1, c1, c2, c3]) ), ct += 1 );
); ); );
return( ct );
}
vector(12, n, a(n) ) \\ Joerg Arndt, Dec 12 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Lorenz H. Menke, Jr., Nov 13 2022
EXTENSIONS
a(26)-a(45) from Hugo Pfoertner, Nov 27 2022
STATUS
approved