This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A174738 #51 Aug 09 2024 11:21:48
%S A174738 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 A174738 46,50,54,58,62,66,70,75,80,85,90,95,100,105,111,117,123,129,135,141,
%U A174738 147,154,161,168,175,182,189,196,204,212,220,228,236
%N A174738 Partial sums of floor(n/7).
%C A174738 Apart from the initial zeros, the same as A011867.
%H A174738 Vincenzo Librandi, <a href="/A174738/b174738.txt">Table of n, a(n) for n = 0..10000</a>
%H A174738 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 A174738 <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 A174738 a(n) = round(n*(n-5)/14).
%F A174738 a(n) = floor((n-2)*(n-3)/14).
%F A174738 a(n) = ceiling((n+1)*(n-6)/14).
%F A174738 a(n) = a(n-7) + n - 6, n > 6.
%F A174738 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 A174738 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 A174738 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 A174738 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 A174738 := proc(n) round(n*(n-5)/14) ; end proc:
%p A174738 seq(A174738(n),n=0..30) ;
%t A174738 Table[Floor[(n - 2)*(n - 3)/14], {n,0,60}] (* _G. C. Greubel_, Dec 13 2016 *)
%o A174738 (Magma) [Round(n*(n-5)/14): n in [0..60]]; // _Vincenzo Librandi_, Jun 22 2011
%o A174738 (PARI) a(n)=(n-2)*(n-3)\14 \\ _Charles R Greathouse IV_, Sep 24 2015
%o A174738 (Sage) [floor((n-2)*(n-3)/14) for n in (0..60)] # _G. C. Greubel_, Aug 31 2019
%o A174738 (GAP) List([0..60], n-> Int((n-2)*(n-3)/14)); # _G. C. Greubel_, Aug 31 2019
%Y A174738 Cf. A001106, A022264, A022265, A024966, A179986, A186029, A218471.
%Y A174738 Cf. Similar sequences: A000217, A002620, A130518, A130519, A130520, A174709, A118729, A218470, A131242.
%K A174738 nonn,easy
%O A174738 0,9
%A A174738 _Mircea Merca_, Nov 30 2010