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A178222
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Partial sums of floor(3^n/4).
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1
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0, 2, 8, 28, 88, 270, 816, 2456, 7376, 22138, 66424, 199284, 597864, 1793606, 5380832, 16142512, 48427552, 145282674, 435848040, 1307544140, 3922632440, 11767897342, 35303692048, 105911076168, 317733228528
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OFFSET
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1,2
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COMMENTS
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Partial sums of A081251(n-1).
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.
Index entries for linear recurrences with constant coefficients, signature (4,-2,-4,3).
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FORMULA
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a(n) = round((3*3^n - 4*n - 4)/8).
a(n) = floor((3*3^n - 4*n - 3)/8).
a(n) = ceiling((3*3^n - 4*n - 5)/8).
a(n) = round((3*3^n - 4*n - 3)/8).
a(n) = a(n-2) + 3^(n-1) - 1, n > 2.
From Bruno Berselli, Jan 14 2011: (Start)
a(n) = (3*3^n - 4*n - 4 + (-1)^n)/8.
G.f.: 2*x^2/((1+x)*(1-3*x)*(1-x)^2). (End)
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EXAMPLE
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a(3) = 0 + 2 + 6 = 8.
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MAPLE
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seq (round ((3*3^n-4*n-3)/8), n=1..25);
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MATHEMATICA
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Accumulate[Floor[3^Range[30]/4]] (* Harvey P. Dale, Nov 04 2011 *)
CoefficientList[Series[2 x/((1 + x) (1 - 3 x) (1 - x)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 26 2014 *)
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PROG
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(Magma) [Floor((3*3^n-4*n-3)/8): n in [1..30]]; // Vincenzo Librandi, Jun 23 2011
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CROSSREFS
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Cf. A081251.
Sequence in context: A118047 A087431 A176758 * A090426 A279193 A280279
Adjacent sequences: A178219 A178220 A178221 * A178223 A178224 A178225
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KEYWORD
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nonn,easy
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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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