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A010036
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Sum of 2^n, ..., 2^(n+1) - 1.
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23
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1, 5, 22, 92, 376, 1520, 6112, 24512, 98176, 392960, 1572352, 6290432, 25163776, 100659200, 402644992, 1610596352, 6442418176, 25769738240, 103079084032, 412316598272, 1649266917376, 6597068718080, 26388276969472, 105553112072192, 422212456677376
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OFFSET
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0,2
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COMMENTS
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Sum of all proper binary numbers with n digits (i.e. those not beginning with 0). Cf. A101291 Sum of all numbers with n digits [base 10]. - Jonathan Vos Post, Sep 07 2006
a(n)/2^n gives the average eccentricity of the graphs of the Chinese rings puzzle with n+1 rings (also known as baguenaudier). - Daniele Parisse, Jun 02 2008
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LINKS
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FORMULA
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a(n) = 6*a(n-1)-8*a(n-2) for n > 1; a(0) = 1, a(1) = 5.
G.f.: (1-x)/((1-2*x)*(1-4*x)). (End)
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MAPLE
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f:= n-> 3*2^(2*n-1)-2^(n-1): seq(f(n), n=0..30);
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MATHEMATICA
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Table[2^n (2^n+(2^(n+1)-1))/2, {n, 0, 25}] (* or *) LinearRecurrence[{6, -8}, {1, 5}, 30] (* Harvey P. Dale, Jan 23 2012 *)
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PROG
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(Magma) [ &+[ k: k in [2^n..2^(n+1)-1] ]: n in [0..21] ]; // Klaus Brockhaus, Nov 27 2009
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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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Steve King (ITTTUCSON(AT)aol.com)
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STATUS
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approved
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