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A087323
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a(n) = (n+1) * 2^n - 1.
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6
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0, 3, 11, 31, 79, 191, 447, 1023, 2303, 5119, 11263, 24575, 53247, 114687, 245759, 524287, 1114111, 2359295, 4980735, 10485759, 22020095, 46137343, 96468991, 201326591, 419430399, 872415231, 1811939327, 3758096383, 7784628223, 16106127359, 33285996543, 68719476735
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = (n + 1) * 2^n - 1 = 2^n * n + 2^n - 1.
a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3). G.f.: x*(3-4*x)/((1-x)*(1-2*x)^2). - Colin Barker, Mar 23 2012
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MATHEMATICA
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LinearRecurrence[{5, -8, 4}, {0, 3, 11}, 40] (* Harvey P. Dale, Sep 15 2019 *)
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PROG
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CROSSREFS
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Cf. A087322 (a triangle which includes this sequence as the leading diagonal but without the initial zero).
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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Formula promoted to definition and offset adjusted to 0 by Alonso del Arte, Jan 31 2014
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STATUS
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approved
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