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%I #47 Sep 08 2022 08:45:51
%S 0,0,0,0,0,0,0,1,2,3,4,5,6,7,9,11,13,15,17,19,21,24,27,30,33,36,39,42,
%T 46,50,54,58,62,66,70,75,80,85,90,95,100,105,111,117,123,129,135,141,
%U 147,154,161,168,175,182,189,196,204,212,220,228,236
%N Partial sums of floor(n/7).
%C Apart from the initial zeros, the same as A011867.
%H Vincenzo Librandi, <a href="/A174738/b174738.txt">Table of n, a(n) for n = 0..10000</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_09">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,0,1,-2,1).
%F a(n) = round(n*(n-5)/14).
%F a(n) = floor((n-2)*(n-3)/14).
%F a(n) = ceiling((n+1)*(n-6)/14).
%F a(n) = a(n-7) + n - 6, n > 6.
%F a(n) = +2*a(n-1) - a(n-2) + a(n-7) - 2*a(n-8) + a(n-9). - _R. J. Mathar_, Nov 30 2010
%F G.f.: x^7/( (1 + x + x^2 + x^3 + x^4 + x^5 + x^6)*(1-x)^3 ). - _R. J. Mathar_, Nov 30 2010
%F a(7n) = A001106(n), a(7n+1) = A218471(n), a(7n+2) = A022264(n), a(7n+3) = A022265(n), a(7n+4) = A186029(n), a(7n+5) = A179986(n), a(7n+6) = A024966(n). - _Philippe Deléham_, Mar 26 2013
%e a(9) = floor(0/7) + floor(1/7) + floor(2/7) + floor(3/7) + floor(4/7) + floor(5/7) + floor(6/7) + floor(7/7) + floor(8/7) + floor(9/7) = 3.
%p A174738 := proc(n) round(n*(n-5)/14) ; end proc:
%p seq(A174738(n),n=0..30) ;
%t Table[Floor[(n - 2)*(n - 3)/14], {n,0,60}] (* _G. C. Greubel_, Dec 13 2016 *)
%o (Magma) [Round(n*(n-5)/14): n in [0..60]]; // _Vincenzo Librandi_, Jun 22 2011
%o (PARI) a(n)=(n-2)*(n-3)\14 \\ _Charles R Greathouse IV_, Sep 24 2015
%o (Sage) [floor((n-2)*(n-3)/14) for n in (0..60)] # _G. C. Greubel_, Aug 31 2019
%o (GAP) List([0..60], n-> Int((n-2)*(n-3)/14)); # _G. C. Greubel_, Aug 31 2019
%Y Cf. A001106, A022264, A022265, A024966, A179986, A186029, A218471.
%Y Cf. Similar sequences: A000217, A002620, A130518, A130519, A130520, A174709, A118729, A218470, A131242.
%K nonn,easy
%O 0,9
%A _Mircea Merca_, Nov 30 2010
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