A144139 Chebyshev polynomial of the second kind U(4,n).

1, 5, 209, 1189, 3905, 9701, 20305, 37829, 64769, 104005, 158801, 232805, 330049, 454949, 612305, 807301, 1045505, 1332869, 1675729, 2080805, 2555201, 3106405, 3742289, 4471109, 5301505, 6242501, 7303505, 8494309, 9825089, 11306405

Offset

0,2

Links

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

Formula

G.f.: (1 + 194*x^2 + 184*x^3 + 5*x^4)/(1 - x)^5. - Vincenzo Librandi, May 29 2014

a(n) = 16*n^4-12*n^2+1 = (4*n^2-2*n-1)*(4*n^2+2*n-1). - Vincenzo Librandi, May 29 2014

From Klaus Purath, Sep 08 2022: (Start)

a(n) = A165900(2*n)*A165900(2*n+1).

a(n) = A057722(2*n).

a(n) = 4*(Sum_{i=1..n} A193250(i)) + 1 = 4*A079414(n) + 1.

(End)

Mathematica

lst={}; Do[AppendTo[lst, ChebyshevU[4, n]], {n, 0, 9^2}]; lst
CoefficientList[Series[(1 + 194 x^2 + 184 x^3 + 5 x^4)/(1 - x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, May 29 2014 *)

Prog

(Magma) [16*n^4-12*n^2+1: n in [0..40]]; // Vincenzo Librandi, May 29 2014

Crossrefs

Cf. A057722, A079414, A165900, A193250.

Sequence in context: A162087 A292330 A068531 * A020541 A006413 A055316

Adjacent sequences: A144136 A144137 A144138 * A144140 A144141 A144142

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Sep 11 2008

Extensions

Changed offset from 1 to 0 by Vincenzo Librandi, May 29 2014

Status

approved