A144138 Chebyshev polynomial of the second kind U(3,n).

0, 4, 56, 204, 496, 980, 1704, 2716, 4064, 5796, 7960, 10604, 13776, 17524, 21896, 26940, 32704, 39236, 46584, 54796, 63920, 74004, 85096, 97244, 110496, 124900, 140504, 157356, 175504, 194996, 215880, 238204, 262016, 287364, 314296, 342860, 373104, 405076

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

G.f.: 4*x*(1 + 10*x + x^2)/(1 - x)^4. - Vincenzo Librandi, May 29 2014

a(n) = 4*n*(2*n^2-1). - Vincenzo Librandi, May 29 2014

Mathematica

Table[ChebyshevU[3, n], {n, 0, 100}] (* and *) Table[4n*(2*n^2-1), {n, 0, 100}]
CoefficientList[Series[4 x (1 + 10 x + x^2)/(1 - x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, May 29 2014 *)
LinearRecurrence[{4, -6, 4, -1}, {0, 4, 56, 204}, 40] (* Harvey P. Dale, Dec 23 2022 *)

Prog

(Magma) [8*n^3-4*n: n in [0..40]]; // Vincenzo Librandi, May 29 2014

Crossrefs

Cf. A100551, A123027, A144139.

Sequence in context: A189864 A360262 A192845 * A331776 A006592 A201448

Adjacent sequences: A144135 A144136 A144137 * A144139 A144140 A144141

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Sep 11 2008

Status

approved