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A178742
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Partial sums of floor(2^n/9).
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2
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0, 0, 0, 0, 1, 4, 11, 25, 53, 109, 222, 449, 904, 1814, 3634, 7274, 14555, 29118, 58245, 116499, 233007, 466023, 932056, 1864123, 3728258, 7456528, 14913068, 29826148, 59652309, 119304632, 238609279, 477218573, 954437161
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OFFSET
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0,6
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COMMENTS
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Partial sums of A153234.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..240
Index to sequences with linear recurrences with constant coefficients, signature (4,-5,1,4,-5,2).
Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.
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FORMULA
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a(n) = round((8*2^n-18*n-9)/36).
a(n) = floor((4*2^n-9*n+2)/18).
a(n) = ceil((4*2^n-9*n-11)/18).
a(n) = round((4*2^n-9*n-4)/18).
a(n) = a(n-6) + 7*2^(n-5)-3 , n>5.
a(n) = 4*a(n-1)-5*a(n-2)+a(n-3)+4*a(n-4)-5*a(n-5)+2*a(n-6).
G.f.: -x^4 / ( (2*x-1)*(1+x)*(x^2-x+1)*(x-1)^2 ).
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EXAMPLE
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a(6)=0+0+0+0+1+3+7=11.
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MAPLE
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A178742 := proc(n) add( floor(2^i/9), i=0..n) ; end proc:
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PROG
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(MAGMA) [&+[Floor(2^k/9): k in [0..n]]: n in [0..25]]; // Bruno Berselli, Apr 26 2011
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CROSSREFS
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Cf. A153234
Sequence in context: A014173 A209232 A156127 * A202088 A079467 A140897
Adjacent sequences: A178739 A178740 A178741 * A178743 A178744 A178745
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KEYWORD
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nonn,less
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AUTHOR
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Mircea Merca, Dec 26 2010
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STATUS
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approved
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