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

Author

Vladimir Joseph Stephan Orlovsky, Sep 11 2008

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A100551, A123027, A144139.

Programs

Magma

[8*n^3-4*n: n in [0..40]]; // 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 *)

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