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A049775
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a(n) is the sum of all integers from 2^(n-2)+1 to 2^(n-1).
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10
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2, 7, 26, 100, 392, 1552, 6176, 24640, 98432, 393472, 1573376, 6292480, 25167872, 100667392, 402661376, 1610629120, 6442483712, 25769869312, 103079346176, 412317122560, 1649267965952, 6597070815232, 26388281163776
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OFFSET
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2,1
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COMMENTS
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Also sum of integers of which the binary order [A029837] is n: a(n) = Sum_[x | ceiling(log_2(x)) = n ]. E.g., a(7) = 6176 = Apply[Plus, Table[w,{w,65,128}]].
This sequence may be obtained by filling a complete binary tree left-to-right, row by row with the integers onwards from 2 and then collecting the sums of the rows; e.g., 2, 3+4, 5+6+7+8, 9+10+11+12+13+14+15+16, etc. a(n) is then equal to the sum of row n-1. - Carl R. White, Aug 19 2003
If the offset is set to zero, the inverse binomial transform gives A007051 without its leading 1. - R. J. Mathar, Mar 26 2009
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LINKS
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FORMULA
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a(n+1) = 4*a(n) - 2^(n-2); see also A007582.
a(n) = 6*a(n-1) - 8*a(n-2).
G.f.: -x^2*(-2+5*x)/((4*x-1)*(2*x-1)). (End)
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EXAMPLE
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a(2) = 2 = 2.
a(3) = 7 = 3 + 4.
a(4) =26 = 5 + 6 + 7 + 8.
..
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MATHEMATICA
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LinearRecurrence[{6, -8}, {2, 7}, 30] (* Harvey P. Dale, Mar 04 2013 *)
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CROSSREFS
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Cf. A049773 (sequence motivating the original definition).
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KEYWORD
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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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