A242851 64*n^6 - 80*n^4 + 24*n^2 - 1.

-1, 7, 2911, 40391, 242047, 950599, 2883167, 7338631, 16451071, 33489287, 63202399, 112211527, 189447551, 306634951, 478821727, 724955399, 1068505087, 1538129671, 2168392031, 3000519367, 4083209599, 5473483847, 7237584991, 9451922311, 12204062207, 15593764999

Offset: 0

Author

Vincenzo Librandi, May 29 2014

Keywords

• sign
• easy

Comments

Chebyshev polynomial of the second kind U(6,n).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000466, A144138, A144139, A242850.

Programs

Magma

[64*n^6-80*n^4+24*n^2-1: n in [0..40]];

Mathematica

Table[64 n^6 - 80 n^4 + 24 n^2 - 1, {n, 0, 40}] (* or *) Table[ChebyshevU[6, n], {n, 0, 40}]

Formula

G.f.: (-1 + 14*x + 2841*x^2 + 20196*x^3 + 20161*x^4 + 2862*x^5 + 7*x^6)/(1 - x)^7.

a(n) = (8*n^3-4*n^2-4*n+1)*(8*n^3+4*n^2-4*n-1).

Extensions

Edited by Bruno Berselli, May 29 2014