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A176758
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a(n) = Sum_{k=0..floor((n-1)/2)} (3^k-1)*binomial(n, 2*k+1).
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1
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2, 8, 28, 88, 264, 768, 2192, 6176, 17248, 47872, 132288, 364416, 1001600, 2748416, 7532800, 20627968, 56452608, 154423296, 422276096, 1154447360, 3155544064, 8624177152, 23567831040, 64400793600, 175970803712, 480810303488
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OFFSET
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3,1
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LINKS
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FORMULA
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G.f.: 2*x^3/( (1-2*x)*(1-2*x-2*x^2) ). (End)
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MATHEMATICA
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(* First program *)
a[n_, q_]:= Sum[(q^((m-1)/2) - 1)*Binomial[n, m], {m, 1, n, 2}];
Table[a[n, 3], {n, 3, 30}]
(* Second program *)
A002605[n_]:= (-I*Sqrt[2])^(n-1)*ChebyshevU[n-1, I/Sqrt[2]];
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PROG
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(Magma) I:=[2, 8, 28]; [n le 3 select I[n] else 4*Self(n-1) - 2*Self(n-2) +4*Self(n-3): n in [1..31]]; // G. C. Greubel, Sep 17 2021
(Sage) [(-i*sqrt(2))^(n-1)*chebyshev_U(n-1, i/sqrt(2)) - 2^(n-1) for n in (3..30)] # G. C. Greubel, Sep 17 2021
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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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