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Search: id:A020540
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| 4, 56, 496, 4064, 32704, 262016, 2096896, 16776704, 134216704, 1073739776, 8589930496, 68719468544, 549755797504, 4398046478336, 35184372023296, 281474976579584, 2251799813423104, 18014398508957696, 144115188074807296
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OFFSET
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0,1
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COMMENT
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Third Chebyshev polynomial second kind evaluated at 2^n.
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LINKS
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Index entries for sequences related to Chebyshev polynomials.
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FORMULA
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G.f.: 4(1+4x)/(1-10x+16x^2).
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EXAMPLE
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U_3(x)=8x^3-4x so U_3(2^n)=8(2^n)^3-4(2^n)=8^(n+1)-2^(n+2).
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MAPLE
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with(orthopoly):seq(U(3, 2^i), i=0..24);
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MATHEMATICA
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Table[ChebyshevU[3, 2^n], {n, 1, 40}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 03 2009]
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PROGRAM
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(PARI) a(n)=if(n<0, 0, 8^(n+1)-2^(n+2))
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CROSSREFS
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Sequence in context: A144138 A006592 A077122 this_sequence A101540 A026740 A130219
Adjacent sequences: A020537 A020538 A020539 this_sequence A020541 A020542 A020543
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KEYWORD
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nonn
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AUTHOR
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Simon Plouffe (simon.plouffe(AT)gmail.com)
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