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A144129
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ChebyshevT[3,n].
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3
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) = 4*n^3 - 3*n. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 11 2009]
Contribution from Peter Luschny (peter(AT)luschny.de), Jul 12 2009: (Start)
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|. (End)
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
| G.f.: x*(1+22*x+x^2)/(1-x)^4. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 11 2009]
a(n)=Cosh[3*ArcCosh[n]]=Cos[3*ArcCos[n]] [From Artur Jasinski (grafix(AT)csl.pl), Feb 14 2010]
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MAPLE
| a := n -> (4*n^2-3)*n; [From Peter Luschny (peter(AT)luschny.de), Jul 12 2009]
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MATHEMATICA
| lst={}; Do[AppendTo[lst, ChebyshevT[3, n]], {n, 0, 10^2}]; lst
Round[Table[N[Cosh[3 ArcCosh[n]], 100], {n, 0, 20}]] [From Artur Jasinski (grafix(AT)csl.pl), Feb 14 2010]
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PROG
| (MAGMA) [ 4*n^3-3*n: n in [0..36] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 11 2009]
(PARI) a(n) = 4*n^3-3*n \\ Charles R Greathouse IV, Feb 08 2012
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CROSSREFS
| Sequence in context: A095796 A175549 A159541 * A026915 A136293 A065013
Adjacent sequences: A144126 A144127 A144128 * A144130 A144131 A144132
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 11 2008
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