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A173645 Partial sums of floor(n^2/11).

%I A173645 #29 Oct 20 2022 21:48:11
%S A173645 0,0,0,0,1,3,6,10,15,22,31,42,55,70,87,107,130,156,185,217,253,293,
%T A173645 337,385,437,493,554,620,691,767,848,935,1028,1127,1232,1343,1460,
%U A173645 1584,1715,1853,1998,2150,2310,2478,2654,2838,3030,3230,3439,3657,3884
%N A173645 Partial sums of floor(n^2/11).
%H A173645 Bruno Berselli, <a href="/A173645/b173645.txt">Table of n, a(n) for n = 0..5000</a>
%H A173645 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 A173645 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,0,0,0,0,0,0,0,1,-3,3,-1).
%F A173645 a(n) = round((2*n^3 + 3*n^2 - 23*n - 12)/66).
%F A173645 a(n) = floor((2*n^3 + 3*n^2 - 23*n + 18)/66).
%F A173645 a(n) = ceiling((2*n^3 + 3*n^2 - 23*n - 42)/66).
%F A173645 a(n) = a(n-11) + (n-5)^2 + 6, n > 10.
%F A173645 From _R. J. Mathar_, Nov 24 2010: (Start)
%F A173645 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).
%F A173645 G.f.: x^4*(x+1)*(x^4 - x^3 + x^2 - x + 1) / ((x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x-1)^4). (End)
%e A173645 a(6) = 6 = 0 + 0 + 0 + 0 + 1 + 2 + 3.
%p A173645 A173645(n):=round((2*n^3+3*n^2-23*n-12)/66)
%t A173645 Accumulate[Floor[Range[0,50]^2/11]] (* _Harvey P. Dale_, Sep 23 2015 *)
%o A173645 (Magma) [ &+[Floor(k^2/11): k in [0..n]]: n in [0..60] ];  // _Bruno Berselli_, Apr 28 2011
%o A173645 (PARI) vector(60, n, n--; (2*n^3+3*n^2-23*n+18)\66) \\ _G. C. Greubel_, Jul 02 2019
%o A173645 (Sage) [floor((2*n^3+3*n^2-23*n+18)/66) for n in (0..60)] # _G. C. Greubel_, Jul 02 2019
%K A173645 nonn,easy
%O A173645 0,6
%A A173645 _Mircea Merca_, Nov 24 2010