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Search: id:A144129
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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; listen)
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OFFSET
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0,3
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COMMENT
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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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FORMULA
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G.f.: x*(1+22*x+x^2)/(1-x)^4. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 11 2009]
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MAPLE
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a := n -> (4*n^2-3)*n; [From Peter Luschny (peter(AT)luschny.de), Jul 12 2009]
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MATHEMATICA
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lst={}; Do[AppendTo[lst, ChebyshevT[3, n]], {n, 0, 10^2}]; lst
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PROGRAM
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(MAGMA) [ 4*n^3-3*n: n in [0..36] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 11 2009]
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CROSSREFS
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Sequence in context: A010014 A095796 A159541 this_sequence A026915 A136293 A065013
Adjacent sequences: A144126 A144127 A144128 this_sequence A144130 A144131 A144132
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KEYWORD
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nonn
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AUTHOR
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Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 11 2008
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