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A178420
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Partial sums of floor(2^n/3).
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5
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0, 1, 3, 8, 18, 39, 81, 166, 336, 677, 1359, 2724, 5454, 10915, 21837, 43682, 87372, 174753, 349515, 699040, 1398090, 2796191, 5592393, 11184798, 22369608, 44739229, 89478471, 178956956, 357913926, 715827867, 1431655749, 2863311514
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = round((8*2^n - 6*n - 9)/12).
a(n) = floor((4*2^n - 3*n - 4)/6).
a(n) = ceiling((4*2^n - 3*n - 5)/6).
a(n) = round((4*2^n - 3*n - 4)/6).
a(n) = a(n-2) + 2^(n-1) - 1, n > 2.
a(n) = (8*2^n - 6*n - 9 + (-1)^n)/12.
G.f.: x^2/((1+x)*(1-2*x)*(1-x)^2). (End)
G.f.: Q(0)/(3*(1-x)^2), where Q(k) = 1 - 1/(4^k - 2*x*16^k/(2*x*4^k - 1/(1 + 1/(2*4^k - 8*x*16^k/(4*x*4^k + 1/Q(k+1)))))); (continued fraction). - Sergei N. Gladkovskii, May 21 2013
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EXAMPLE
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a(5) = 0 + 1 + 2 + 5 + 10 = 18.
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MAPLE
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seq(round((4*2^n-3*n-4)/6), n=1..50)
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MATHEMATICA
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CoefficientList[Series[x / ((1 + x) (1 - 2 x) (1 - x)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 26 2014 *)
LinearRecurrence[{3, -1, -3, 2}, {0, 1, 3, 8}, 40] (* or *) Accumulate[ Table[ Floor[ 2^n/3], {n, 40}]] (* Harvey P. Dale, Dec 24 2015 *)
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PROG
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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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