%I #40 Sep 08 2022 08:45:53

%S 0,1,6,40,280,1961,13726,96080,672560,4707921,32955446,230688120,

%T 1614816840,11303717881,79126025166,553882176160,3877175233120,

%U 27140226631841,189981586422886,1329871104960200,9309097734721400

%N Partial sums of round(7^n/10).

%H Vincenzo Librandi, <a href="/A178397/b178397.txt">Table of n, a(n) for n = 0..400</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_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-8,8,-7).

%F a(n) = round((7*7^n-7)/60) = round((7*7^n+5)/60).

%F a(n) = floor((7*7^n+17)/60).

%F a(n) = ceiling((7*7^n-7)/60).

%F a(n) = a(n-4) + 40*7^(n-3), n > 3.

%F a(n) = 8*a(n-1) - 8*a(n-2) + 8*a(n-3) - 7*a(n-4), n > 3.

%F G.f.: -(2*x^2-x)/((x-1)*(7*x-1)*(x^2+1)).

%e a(4) = 0 + 1 + 5 + 34 + 240 = 280.

%p A178397 := proc(n) add( round(7^i/10),i=0..n) ; end proc:

%t Accumulate[Floor[7^Range[0,20]/10+1/2]] (* _Harvey P. Dale_, Aug 20 2011 *)

%o (Magma) [Round((7*7^n-7)/60): n in [0..40]]; // _Vincenzo Librandi_, Jun 23 2011

%o (PARI) a(n) = (7*7^n+17)\60; \\ _Altug Alkan_, Sep 21 2018

%K nonn,less

%O 0,3

%A _Mircea Merca_, Dec 28 2010