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 A144139 Chebyshev polynomial of the second kind U(4,n). 9
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 16 23:59 EDT 2024. Contains 375984 sequences. (Running on oeis4.)