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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).
2

%I #31 Jan 02 2023 09:01:55

%S 47,271,810,1849,3395,5832,8915,13242,18465,25267,32874,43023,53662,

%T 66957,81770,99374,117564,140303,163048,190757,219702,252465,285820,

%U 326853,366732

%N 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).

%o (PARI){ a(n) = \\ A358399

%o my( ct = 0 );

%o for (c1 = -n, n,

%o for (c2 = -n, n,

%o for (c3 = -n, n,

%o for (c4 = -n, n,

%o if ( ! polisirreducible( Pol([1,c1,c2,c3,c4]) ), ct += 1 );

%o ); ); ); );

%o return( ct );

%o }

%o vector(12, n, a(n) )

%o \\ _Joerg Arndt_, Dec 05 2022

%Y Cf. A358398, A358400, A067274.

%K nonn,more

%O 1,1

%A _Lorenz H. Menke, Jr._, Nov 13 2022