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A091928
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a(0)=1, a(1)=5; a(n) = 6*a(n-1) + 5*a(n-2) for n > 1.
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4
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1, 5, 35, 235, 1585, 10685, 72035, 485635, 3273985, 22072085, 148802435, 1003175035, 6763062385, 45594249485, 307380808835, 2072256100435, 13970440646785, 94183924382885, 634955749531235, 4280654119101835
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OFFSET
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0,2
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COMMENTS
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Let the generator matrix for the ternary Golay G_12 code be [I|B], where the elements of B are taken from the set {0,1,2}. Then a(n)=sum of first row of B^n.
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LINKS
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FORMULA
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G.f.: (1-x)/(1-6x-5x^2).
a(n) = (3+sqrt(14))^n(1/sqrt(14)+1/2) + (3-sqrt(14))^n(1/2-1/sqrt(14)).
a(n) = Sum_{k=0..n} 5^k*A122542(n,k). Lim_{n->infinity} a(n+1)/a(n) = 3 + sqrt(14) = 6.741657386773.... - Philippe Deléham, Sep 22 2006
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MATHEMATICA
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LinearRecurrence[{6, 5}, {1, 5}, 30] (* Harvey P. Dale, Apr 09 2022 *)
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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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EXTENSIONS
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STATUS
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approved
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