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A175829 Partial sums of ceiling(n^2/11).

%I A175829 #20 Sep 08 2022 08:45:52
%S A175829 0,1,2,3,5,8,12,17,23,31,41,52,66,82,100,121,145,172,202,235,272,313,
%T A175829 357,406,459,516,578,645,717,794,876,964,1058,1157,1263,1375,1493,
%U A175829 1618,1750,1889,2035,2188,2349,2518,2694,2879,3072,3273,3483,3702,3930
%N A175829 Partial sums of ceiling(n^2/11).
%C A175829 Partial sums of A036409.
%H A175829 Vincenzo Librandi, <a href="/A175829/b175829.txt">Table of n, a(n) for n = 0..870</a>
%H A175829 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.
%F A175829 a(n) = round((2*n+1)*(n^2 + n + 18)/66).
%F A175829 a(n) = floor((n+1)*(2*n^2 + n + 36)/66).
%F A175829 a(n) = ceiling((2*n^3 + 3*n^2 + 37*n)/66).
%F A175829 a(n) = a(n-11) + (n+1)*(n-11) + 52, n > 10.
%F A175829 G.f.: x*(1+x)*(x^2 - x + 1)*(x^4 - x^3 + x^2 - x + 1)*(x^4 - x^2 + 1) / ( (x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x-1)^4 ). - _R. J. Mathar_, Dec 06 2010
%F A175829 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-11) - 3*a(n-12) + 3*a(n-13) - a(n-14). - _R. J. Mathar_, Dec 06 2010
%e A175829 a(11) = 0 + 1 + 1 + 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 11 = 52.
%p A175829 seq(round((2*n+1)*(n^2+n+18)/66),n=0..50)
%o A175829 (Magma) [Floor((n+1)*(2*n^2+n+36)/66): n in [0..50]]; // _Vincenzo Librandi_, Apr 29 2011
%Y A175829 Cf. A175822, A175826, A175827.
%K A175829 nonn,easy
%O A175829 0,3
%A A175829 _Mircea Merca_, Dec 05 2010