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A099142
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a(n) = 6^n * T(n, 4/3) where T is the Chebyshev polynomial of the first kind.
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6
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1, 8, 92, 1184, 15632, 207488, 2757056, 36643328, 487039232, 6473467904, 86042074112, 1143628341248, 15200538791936, 202038000386048, 2685388609667072, 35692849740775424, 474411605904392192
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OFFSET
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0,2
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COMMENTS
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In general, r^n * T(n,(r+2)/r) has g.f. (1-(r+2)*x)/(1-2*(r+2)*x + r^2*x^2), e.g.f. exp((r+2)*x)*cosh(2*sqrt(r+1)*x), a(n) = Sum_{k=0..n} (r+1)^k*binomial(2n,2k) and a(n) = (1+sqrt(r+1))^(2*n)/2 + (1-sqrt(r+1))^(2*n)/2.
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LINKS
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FORMULA
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G.f.: (1-8*x)/(1-16*x+36*x^2);
E.g.f.: exp(8*x)*cosh(2*sqrt(7)*x).
a(n) = 6^n * T(n, 8/6) where T is the Chebyshev polynomial of the first kind.
a(n) = Sum_{k=0..n} 7^k * binomial(2n, 2k).
a(n) = (1+sqrt(7))^(2*n)/2 + (1-sqrt(7))^(2*n)/2.
a(0)=1, a(1)=8, a(n) = 16*a(n-1) - 36*a(n-2) for n > 1. - Philippe Deléham, Sep 08 2009
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MATHEMATICA
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LinearRecurrence[{16, -36}, {1, 8}, 20] (* Harvey P. Dale, Mar 09 2018 *)
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PROG
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(PARI) a(n) = 6^n*polchebyshev(n, 1, 4/3); \\ Michel Marcus, Sep 08 2019
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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