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).

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

1,1

Links

Table of n, a(n) for n=1..25.

Prog

(PARI)
{ 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

Crossrefs

Cf. A358398, A358399, A067274.

Sequence in context: A276263 A140791 A377295 * A175017 A271977 A217724

Adjacent sequences: A358397 A358398 A358399 * A358401 A358402 A358403

Keyword

nonn,more

Author

Lorenz H. Menke, Jr., Nov 13 2022

Status

approved