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A178543
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Partial sums of round(3^n/5).
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1
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0, 1, 3, 8, 24, 73, 219, 656, 1968, 5905, 17715, 53144, 159432, 478297, 1434891, 4304672, 12914016, 38742049, 116226147, 348678440, 1046035320, 3138105961, 9414317883, 28242953648, 84728860944, 254186582833
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = round(3^(n+1)/10).
a(n) = floor((3*3^n + 3)/10).
a(n) = ceiling((3*3^n - 3)/10).
a(n) = a(n-4) + 8*3^(n-3), n > 3.
a(n) = 3*a(n-1) - a(n-2) + 3*a(n-3), n > 2.
G.f.: x/((1-3*x)*(1+x^2)).
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EXAMPLE
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a(4) = round(1/5) + round(3/5) + round(9/5) + round(27/5) + round(81/5) = 0 + 1 + 2 + 5 + 16 = 24.
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MAPLE
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seq(round(3^n/10), n=1..25);
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MATHEMATICA
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Accumulate[Floor[3^Range[0, 30]/5+1/2]] (* Harvey P. Dale, Jul 02 2011 *)
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PROG
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(PARI) vector(40, n, n--; (3*(3^n +1)/10)\1) \\ G. C. Greubel, Jan 30 2019
(Sage) [floor(3*(3^n+1)/10) for n in range(40)] # G. C. Greubel, Jan 30 2019
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CROSSREFS
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KEYWORD
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nonn,less,easy
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AUTHOR
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STATUS
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approved
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