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A103897
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a(n) = 3*2^(n-1)*(2^n-1).
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4
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3, 18, 84, 360, 1488, 6048, 24384, 97920, 392448, 1571328, 6288384, 25159680, 100651008, 402628608, 1610563584, 6442352640, 25769607168, 103078821888, 412316073984, 1649265868800, 6597066620928, 26388272775168, 105553103683584, 422212439900160
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OFFSET
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1,1
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COMMENTS
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Divide the sequence of natural numbers: s0=1,2,3,4,5,6,7,8,9,10,11,12,13,14,... into sections s(n) of length 2*s1-1, where s1=initial digits of s(n): s={1,2},{3,4,5,6},{7,8,9,10,11,12,13,14},... then a(n)=sum of terms of s(n): 3,18,84,...
Sum of the numbers between 2^n and 2^(n+1), both excluded. - Gionata Neri, Jun 16 2015
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LINKS
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FORMULA
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G.f.: 3*x/((1-2*x)*(1-4*x)).
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MATHEMATICA
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Table[3*2^(n - 1)*(2^n - 1), {n, 30}]
LinearRecurrence[{6, -8}, {3, 18}, 30] (* Harvey P. Dale, Feb 11 2018 *)
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PROG
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(Magma) [3*2^(n-1)*(2^n-1): n in [1..24]]; // Bruno Berselli, Sep 19 2011
(Python) b = list(range(0, 2**20-1)); a = [sum(b[2**i-1:2**(i+1)-1]) for i in range(1, 20)] ## Johan Claes, Nov 10 2019
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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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