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A178222 Partial sums of floor(3^n/4). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Partial sums of A081251(n-1).
LINKS
Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.
FORMULA
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)
EXAMPLE
a(3) = 0 + 2 + 6 = 8.
MAPLE
seq (round ((3*3^n-4*n-3)/8), n=1..25);
MATHEMATICA
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 *)
PROG
(Magma) [Floor((3*3^n-4*n-3)/8): n in [1..30]]; // Vincenzo Librandi, Jun 23 2011
CROSSREFS
Cf. A081251.
Sequence in context: A118047 A087431 A176758 * A090426 A279193 A280279
KEYWORD
nonn,easy
AUTHOR
Mircea Merca, Dec 26 2010
STATUS
approved

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Last modified March 29 09:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)