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A144129
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ChebyshevT(3, n).
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15
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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
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OFFSET
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0,3
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COMMENTS
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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
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LINKS
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FORMULA
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a(n) = cosh(3*arccosh(n)) = cos(3*arccos(n)). - Artur Jasinski, Feb 14 2010
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MAPLE
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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