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 A178543 Partial sums of round(3^n/5). 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..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 (3,-1,3). FORMULA 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)). a(n) = 3^(n+1)/10 - (-1)^n* A112030(n)/10. - R. J. Mathar, Jan 08 2011 EXAMPLE a(4) = round(1/5) + round(3/5) + round(9/5) + round(27/5) + round(81/5) = 0 + 1 + 2 + 5 + 16 = 24. MAPLE seq(round(3^n/10), n=1..25); MATHEMATICA Accumulate[Floor[3^Range[0, 30]/5+1/2]] (* Harvey P. Dale, Jul 02 2011 *) PROG (Magma) [Round(3^(n+1)/10): n in [0..40]]; // Vincenzo Librandi, Jun 21 2011 (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 CROSSREFS Cf. A112030. Sequence in context: A080923 A118264 A006365 * A188175 A046919 A291886 Adjacent sequences: A178540 A178541 A178542 * A178544 A178545 A178546 KEYWORD nonn,less,easy AUTHOR Mircea Merca, Dec 28 2010 STATUS approved

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Last modified December 4 18:21 EST 2023. Contains 367563 sequences. (Running on oeis4.)