A178711 - OEIS

%I #27 Sep 08 2022 08:45:54

%S 0,3,20,109,555,2787,13947,69750,348767,1743856,8719302,43596534,

%T 217982694,1089913497,5449567514,27247837603,136239188049,

%U 681195940281,3405979701441,17029898507244,85149492536261,425747462681350,2128737313406796,10643686567034028,53218432835170188

%N Partial sums of floor(5^n/7).

%H Vincenzo Librandi, <a href="/A178711/b178711.txt">Table of n, a(n) for n = 1..500</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_06">Index entries for linear recurrences with constant coefficients</a>, signature (7,-11,4,7,-11,5).

%F a(n) = round((5*5^n - 14*n - 14)/28).

%F a(n) = floor((5*5^n - 14*n - 5)/28).

%F a(n) = ceiling((5*5^n - 14*n - 23)/28).

%F a(n) = a(n-6) + 558*5^(n-5) - 3, n > 6.

%F G.f.: -x^2*(2*x^2 - x + 3)/((x-1)^2*(x+1)*(5*x-1)*(x^2-x+1)). [_Colin Barker_, Oct 27 2012]

%e a(7) = 0 + 3 + 17 + 89 + 446 + 2232 + 11160 = 13947.

%p seq(floor((5*5^n-14*n-5)/28),n=1..25)

%t Accumulate[Floor[5^Range[30]/7]] (* or *) LinearRecurrence[{7,-11,4,7,-11,5},{0,3,20,109,555,2787},30] (* _Harvey P. Dale_, May 27 2018 *)

%o (Magma) [Round((5*5^n-14*n-14)/28): n in [1..30]]; // _Vincenzo Librandi_, Jun 21 2011

%o (PARI) vector(30, n, ((5^(n+1)-14*n-5)/28)\1) \\ _G. C. Greubel_, Jan 24 2019

%o (Sage) [floor((5^(n+1)-14*n-5)/28) for n in (1..30)] # _G. C. Greubel_, Jan 24 2019

%K nonn,easy

%O 1,2

%A _Mircea Merca_, Dec 26 2010