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A358398
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a(n) is the number of reducible monic cubic polynomials x^3 + r*x^2 + s*x + t with integer coefficients bounded by naïve height n (abs(r), abs(s), abs(t) <= n).
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2
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15, 53, 117, 215, 329, 493, 657, 877, 1103, 1383, 1643, 2017, 2325, 2721, 3131, 3601, 4009, 4575, 5031, 5647, 6221, 6849, 7409, 8211, 8849, 9593, 10335, 11199, 11899, 12915, 13671, 14655, 15559, 16535, 17473, 18711, 19619, 20711, 21787, 23099, 24095, 25507, 26571, 27931, 29259
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OFFSET
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1,1
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LINKS
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FORMULA
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Dubickas (2014) shows that a(n) ~ 2(1+(2/3)Pi^2)n^2 = 15.1598... n^2 for large n.
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PROG
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(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 );
}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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