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A165324
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a(0)=1, a(1)=9, a(n)= 19*a(n-1)-81*a(n-2) for n>1.
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2
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1, 9, 90, 981, 11349, 136170, 1667961, 20661489, 257463450, 3218224941, 40291734429, 504866733930, 6328837455921, 79353706214169, 995084584139610, 12478956895304901, 156498329695484709, 1962672755694512490
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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 (19+sqrt(37))/2 = 12.5413812...
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LINKS
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FORMULA
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G.f.: (1-10x)/(1-19x+81x^2). a(n)= Sum_{k, 0<=k<=n}A165253(n,k)*9^(n-k).
a(n) = ((37-sqrt(37))*(19+sqrt(37))^n+(37+sqrt(37))*(19-sqrt(37))^n)/(74*2^n). [From Klaus Brockhaus, Sep 28 2009]
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MATHEMATICA
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LinearRecurrence[{19, -81}, {1, 9}, 20] (* Harvey P. Dale, Nov 20 2020 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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