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%I #32 Sep 08 2022 08:45:54
%S 0,1,6,22,70,215,652,1964,5900,17709,53138,159426,478290,1434883,
%T 4304664,12914008,38742040,116226137,348678430,1046035310,3138105950,
%U 9414317871,28242953636,84728860932,254186582820
%N Partial sums of floor(3^n/5).
%H Vincenzo Librandi, <a href="/A178706/b178706.txt">Table of n, a(n) for n = 1..700</a>
%H 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 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-8,8,-7,3).
%F a(n) = round((3*3^n - 5*n - 5)/10).
%F a(n) = floor((3*3^n - 5*n - 3)/10).
%F a(n) = ceiling((3*3^n - 5*n - 7)/10).
%F a(n) = round((3*3^n - 5*n - 3)/10).
%F a(n) = a(n-4) + 8*3^(n-3) - 2, n > 4.
%F a(n) = 5*a(n-1) - 8*a(n-2) + 8*a(n-3) - 7*a(n-4) + 3*a(n-5), n > 5.
%F G.f.: x^2*(1+x) / ( (1-3*x)*(1+x^2)*(1-x)^2 ).
%e a(5) = 0 + 1 + 5 + 16 + 48 = 70.
%p A178706 := proc(n) add( floor(3^i/5),i=0..n) ; end proc:
%t Table[Floor[(3^(n+1)-5*n-3)/10], {n,1,30}] (* _G. C. Greubel_, Jan 25 2019 *)
%o (Magma) [Round((3*3^n-5*n-5)/10): n in [1..30]]; // _Vincenzo Librandi_, Jun 21 2011
%o (PARI) vector(30, n, ((3^(n+1)-5*n-3)/10)\1) \\ _G. C. Greubel_, Jan 25 2019
%o (Sage) [floor((3^(n+1)-5*n-3)/10) for n in (1..30)] # _G. C. Greubel_, Jan 25 2019
%K nonn,less
%O 1,3
%A _Mircea Merca_, Dec 26 2010
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