id:A086375 - OEIS Search Results

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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.

+0
2

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, 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, 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 (list; graph; listen)

	OFFSET	`1,2`
	EXAMPLE	`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).`
	PROGRAM	`(PARI) p2 = 1; p1 = 2x; for (n = 1, 103, p = 2x*p1 - p2; f = factor(p1 + 1); print(sum(i = 1, matsize(f)[1], f[i, 2]), " "); p2 = p1; p1 = p); (Wasserman)`
	CROSSREFS	`Cf. A086327.` `Cf. A086374.` `Sequence in context: A144370 A087050 A065770 this_sequence A107324 A023522 A066241` `Adjacent sequences: A086372 A086373 A086374 this_sequence A086376 A086377 A086378`
	KEYWORD	`nonn,easy`
	AUTHOR	`Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 06 2003`
	EXTENSIONS	`More terms from David Wasserman (wasserma(AT)spawar.navy.mil) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 02 2005`

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Last modified November 21 14:49 EST 2008. Contains 150807 sequences.

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