A085640 Resultant of the polynomial x^3-1 and the Chebyshev polynomial of the first kind T_n(x).

1, 7, 37, 193, 1021, 5383, 28393, 149761, 789913, 4166407, 21975757, 115911361, 611375701, 3224707591, 17008754257, 89712854017, 473191396273, 2495853018631, 13164403113973, 69435783298753, 366239772557101

Offset: 1

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 15 2003

Keywords

• nonn

Crossrefs

Cf. A086840.

Programs

PARI

Tnmin2 = 1; Tnmin1 = x; print1(polresultant(x^3 - 1, Tnmin1), ", "); for (n = 2, 30, T = 2*x*Tnmin1 - Tnmin2; print1(polresultant(x^3 - 1, T), ", "); Tnmin2 = Tnmin1; Tnmin1 = T); \\ David Wasserman, Feb 08 2005

Formula

From Creighton Dement, Jan 17 2009: (Start)

G.f.: (1+3*x+3*x^2-x^3)/(1-4*x-6*x^2-4*x^3+x^4) (conjecture).

Generating floretion C*F with C = 0.5('k + k' - 'j - j' - ki - 2ii - ik - ij - ji) and F = .5('k + ki + 'j + ji). (End)

Extensions

More terms from David Wasserman, Feb 08 2005