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 A144129 ChebyshevT(3, n). 12
 0, 1, 26, 99, 244, 485, 846, 1351, 2024, 2889, 3970, 5291, 6876, 8749, 10934, 13455, 16336, 19601, 23274, 27379, 31940, 36981, 42526, 48599, 55224, 62425, 70226, 78651, 87724, 97469, 107910, 119071, 130976, 143649, 157114, 171395, 186516 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The general formula for alternating sums of powers of odd integers is in terms of the Swiss-Knife polynomials P(n,x) A153641 (P(n,0)-(-1)^k*P(n,2*k))/2. Here n=3, thus a(k) = |(P(3,0)-(-1)^k*P(3,2*k))/2|. - Peter Luschny, Jul 12 2009 Partial sums of A069190. - J. M. Bergot, Jul 13 2013 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 a(n) = 4*n^3 - 3*n. - Klaus Brockhaus, Jan 11 2009 G.f.: x*(1+22*x+x^2)/(1-x)^4. - Klaus Brockhaus, Jan 11 2009 a(n) = cosh(3*arccosh(n)) = cos(3*arccos(n)). - Artur Jasinski, Feb 14 2010 a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - Vincenzo Librandi, Jun 30 2012 MAPLE a := n -> (4*n^2-3)*n; # Peter Luschny, Jul 12 2009 MATHEMATICA lst={}; Do[AppendTo[lst, ChebyshevT[3, n]], {n, 0, 10^2}]; lst Round[Table[N[Cosh[3 ArcCosh[n]], 100], {n, 0, 20}]] (* Artur Jasinski, Feb 14 2010 *) CoefficientList[Series[x*(1+22*x+x^2)/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 30 2012 *) LinearRecurrence[{4, -6, 4, -1}, {0, 1, 26, 99}, 40] (* Harvey P. Dale, Apr 02 2015 *) PROG (MAGMA) [ 4*n^3-3*n: n in [0..36] ]; // Klaus Brockhaus, Jan 11 2009 (PARI) a(n) = 4*n^3-3*n \\ Charles R Greathouse IV, Feb 08 2012 (MAGMA) I:=[0, 1, 26, 99]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 30 2012 CROSSREFS Sequence in context: A256645 A175549 A159541 * A026915 A136293 A065013 Adjacent sequences:  A144126 A144127 A144128 * A144130 A144131 A144132 KEYWORD nonn,easy AUTHOR Vladimir Joseph Stephan Orlovsky, Sep 11 2008 STATUS approved

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Last modified August 17 22:32 EDT 2018. Contains 313817 sequences. (Running on oeis4.)