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A178543 Partial sums of round(3^n/5).

%I A178543 #48 Sep 08 2022 08:45:54
%S A178543 0,1,3,8,24,73,219,656,1968,5905,17715,53144,159432,478297,1434891,
%T A178543 4304672,12914016,38742049,116226147,348678440,1046035320,3138105961,
%U A178543 9414317883,28242953648,84728860944,254186582833
%N A178543 Partial sums of round(3^n/5).
%H A178543 Vincenzo Librandi, <a href="/A178543/b178543.txt">Table of n, a(n) for n = 0..1000</a>
%H A178543 Mircea Merca, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL14/Merca/merca3.html">Inequalities and Identities Involving Sums of Integer Functions</a> J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.
%H A178543 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,3).
%F A178543 a(n) = round(3^(n+1)/10).
%F A178543 a(n) = floor((3*3^n + 3)/10).
%F A178543 a(n) = ceiling((3*3^n - 3)/10).
%F A178543 a(n) = a(n-4) + 8*3^(n-3), n > 3.
%F A178543 a(n) = 3*a(n-1) - a(n-2) + 3*a(n-3), n > 2.
%F A178543 G.f.: x/((1-3*x)*(1+x^2)).
%F A178543 a(n) = 3^(n+1)/10 - (-1)^n* A112030(n)/10. - _R. J. Mathar_, Jan 08 2011
%e A178543 a(4) = round(1/5) + round(3/5) + round(9/5) + round(27/5) + round(81/5) = 0 + 1 + 2 + 5 + 16 = 24.
%p A178543 seq(round(3^n/10),n=1..25);
%t A178543 Accumulate[Floor[3^Range[0,30]/5+1/2]] (* _Harvey P. Dale_, Jul 02 2011 *)
%o A178543 (Magma) [Round(3^(n+1)/10): n in [0..40]]; // _Vincenzo Librandi_, Jun 21 2011
%o A178543 (PARI) vector(40, n, n--; (3*(3^n +1)/10)\1) \\ _G. C. Greubel_, Jan 30 2019
%o A178543 (Sage) [floor(3*(3^n+1)/10) for n in range(40)] # _G. C. Greubel_, Jan 30 2019
%Y A178543 Cf. A112030.
%K A178543 nonn,less,easy
%O A178543 0,3
%A A178543 _Mircea Merca_, Dec 28 2010