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A165224
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a(0)=1, a(1)=9, a(n) = 18*a(n-1) - 49*a(n-2) for n > 1.
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3
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1, 9, 113, 1593, 23137, 338409, 4957649, 72655641, 1064876737, 15607654857, 228758827313, 3352883803641, 49142725927201, 720277760311209, 10557006115168913, 154732499817791193, 2267891697076964737
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OFFSET
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0,2
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COMMENTS
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a(n)/a(n-1) tends to 9 + 4*sqrt(2) = 14.65685424... - Klaus Brockhaus, Sep 25 2009
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LINKS
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FORMULA
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G.f.: (1-9x)/(1-18x+49x^2);
e.g.f.: exp(9x)*cosh(4*sqrt(2)x);
a(n) = Sum_{k=0..n} 8^k*binomial(2n,2k) = Sum_{k=0..n} 8^k*A086645(n,k);
a(n) = 7^n*T(n,9/7) where T is the Chebyshev polynomial of the first kind;
a(n) = (1+sqrt(8))^(2n)/2 + (1-sqrt(8))^(2n)/2.
a(n) = ((9-4*sqrt(2))^n + (9+4*sqrt(2))^n)/2. - Klaus Brockhaus, Sep 25 2009
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MATHEMATICA
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LinearRecurrence[{18, -49}, {1, 9}, 20] (* Harvey P. Dale, Sep 30 2016 *)
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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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