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Number of factors over Q in the factorization of U_n(x) + 1 where U_n(x) is the Chebyshev polynomial of the second kind.

2

`%I #7 Jul 29 2018 10:44:09
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`%S 1,2,2,3,2,4,3,3,3,6,2,4,4,5,4,5,2,7,4,4,4,8,3,4,5,6,4,8,2,8,4,3,6,9,
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`%T 4,5,4,8,4,8,2,8,6,4,6,10,3,6,5,7,4,8,4,10,6,4,4,12,2,6,6,7,8,7,4,8,4,
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`%U 8,4,14,2,5,6,6,8,8,4,12,5,4,5,12,4,6,6,8,4,12,4,10,6,4,6,12,4,6,6,10,6,9
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`%N Number of factors over Q in the factorization of U_n(x) + 1 where U_n(x) is the Chebyshev polynomial of the second kind.
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`%e a(7)=3 because 1+U(7,x)=1+128x^7-192x^5+80x^3-8x=(2x+1)(8x^3-6x+1)(8x^3-4x^2-4x+1).
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`%o (PARI) p2 = 1; p1 = 2*x; for (n = 1, 103, p = 2*x*p1 - p2; f = factor(p1 + 1); print(sum(i = 1, matsize(f)[1], f[i, 2]), " "); p2 = p1; p1 = p); \\ _David Wasserman_, Mar 02 2005
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`%Y Cf. A086327.
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`%Y Cf. A086374.
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`%K nonn,easy
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`%O 1,2
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`%A Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 06 2003
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`%E More terms from _David Wasserman_ and _Emeric Deutsch_, Mar 02 2005
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