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A099035
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a(n) = (n+1)*2^(n-1) - 1.
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9
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1, 5, 15, 39, 95, 223, 511, 1151, 2559, 5631, 12287, 26623, 57343, 122879, 262143, 557055, 1179647, 2490367, 5242879, 11010047, 23068671, 48234495, 100663295, 209715199, 436207615, 905969663, 1879048191, 3892314111, 8053063679
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OFFSET
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1,2
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COMMENTS
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Binomial transform of [1, 4, 6, 8, 10, 12, 14, 16, ...]. Equals A128064 * A000225, (A000225 starting 1, 3, 7, 15, ...). - Gary W. Adamson, Dec 28 2007
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LINKS
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FORMULA
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a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3).
G.f.: x*(1-2*x^2)/((1-x)*(1-2*x)^2). (End)
E.g.f.: ((2*x+1)*exp(2*x) - 2*exp(x) + 1)/2. - G. C. Greubel, Dec 31 2017
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MATHEMATICA
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Table[(n + 1)*2^(n - 1) - 1, {n, 1, 30}] (* G. C. Greubel, Dec 31 2017 *)
LinearRecurrence[{5, -8, 4}, {1, 5, 15}, 30] (* Harvey P. Dale, Dec 28 2022 *)
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PROG
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(Magma) [(n+1)*2^(n-1) -1: n in [1..30]]; // G. C. Greubel, Dec 31 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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