A358399
a(n) is the number of reducible monic quartic polynomials (x^4 + r*x^3 + s*x^2 + t*x + u) with integer coefficients bounded by naïve height n (abs(r), abs(s), abs(t), abs(u) <= n).
Original entry on oeis.org
47, 271, 810, 1849, 3395, 5832, 8915, 13242, 18465, 25267, 32874, 43023, 53662, 66957, 81770, 99374, 117564, 140303, 163048, 190757, 219702, 252465, 285820, 326853, 366732
Offset: 1
-
{ a(n) = \\ A358399
my( ct = 0 );
for (c1 = -n, n,
for (c2 = -n, n,
for (c3 = -n, n,
for (c4 = -n, n,
if ( ! polisirreducible( Pol([1,c1,c2,c3,c4]) ), ct += 1 );
); ); ); );
return( ct );
}
vector(12, n, a(n) )
\\ Joerg Arndt, Dec 05 2022
A358400
a(n) is the number of reducible monic quintic polynomials (x^5 + r*x^4 + s*x^3 + t*x^2 + u*x + v) with integer coefficients bounded by naïve height n (abs(r), abs(s), abs(t), abs(u), abs(v) <= n).
Original entry on oeis.org
139, 1313, 5359, 15365, 34229, 68385, 120421, 200839, 312057, 468827, 669591, 943175, 1274089, 1701441, 2216841, 2856379, 3594651, 4510437, 5541135, 6788823, 8195941, 9845089, 11670925, 13842429, 16191555
Offset: 1
-
{ a(n) = \\ A358400
my( ct = 0 );
for (c1 = -n, n,
for (c2 = -n, n,
for (c3 = -n, n,
for (c4 = -n, n,
for (c5 = -n, n,
if ( ! polisirreducible( Pol([1,c1,c2,c3,c4,c5]) ), ct += 1 );
); ); ); ); );
return( ct );
}
vector(7, n, a(n) )
\\ Joerg Arndt, Dec 05 2022
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