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A191007
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a(n) = n*2^(n+1) + (2^(n+3)+(-1)^n)/3.
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0
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3, 9, 27, 69, 171, 405, 939, 2133, 4779, 10581, 23211, 50517, 109227, 234837, 502443, 1070421, 2271915, 4805973, 10136235, 21321045, 44739243, 93672789, 195734187, 408245589, 850045611, 1767200085, 3668617899, 7605671253, 15748213419, 32570168661, 67287820971
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OFFSET
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0,1
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COMMENTS
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Another renewal type of sequence: Let X, X(1),X(2),... denote independent random variables with pdf P(X=1) = P(X=2) = P(X=4) = 1/3. Let N(x) denote the first value of k such that X(1)*X(2)...*X(k) > x, and let H(x) = E(N(x)). The sequence a(n) is given by a(n) = 2^(n+1)*H(2^n).
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LINKS
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FORMULA
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a(n) = n*2^(n+1) + (2^(n+3)+(-1)^n)/3.
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MATHEMATICA
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Table[n 2^(n + 1) + (2^(n + 3) + (-1)^n)/3, {n, 0, 70}] (* Vincenzo Librandi, Oct 16 2014 *)
LinearRecurrence[{3, 0, -4}, {3, 9, 27}, 40] (* Harvey P. Dale, Feb 11 2024 *)
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PROG
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(PARI) a(n) = n*2^(n+1) + (2^(n+3)+(-1)^n)/3; \\ Michel Marcus, Oct 16 2014
(Magma) [n*2^(n+1)+(2^(n+3)+(-1)^n)/3: n in [0..30]]; // Vincenzo Librandi, Oct 16 2014
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CROSSREFS
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KEYWORD
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nonn,easy,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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