The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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). 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 Adjacent sequences: A178219 A178220 A178221 * A178223 A178224 A178225 KEYWORD nonn,easy AUTHOR Mircea Merca, Dec 26 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 7 01:49 EST 2023. Contains 367616 sequences. (Running on oeis4.)