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A175826 Partial sums of ceiling(n^2/8).

%I A175826 #35 Mar 17 2023 07:13:37
%S A175826 0,1,2,4,6,10,15,22,30,41,54,70,88,110,135,164,196,233,274,320,370,
%T A175826 426,487,554,626,705,790,882,980,1086,1199,1320,1448,1585,1730,1884,
%U A175826 2046,2218,2399,2590,2790,3001,3222,3454,3696,3950,4215,4492,4780,5081,5394
%N A175826 Partial sums of ceiling(n^2/8).
%C A175826 Partial sums of A036406.
%H A175826 Vincenzo Librandi, <a href="/A175826/b175826.txt">Table of n, a(n) for n = 0..860</a>
%H A175826 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 A175826 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,1,-3,3,-1).
%F A175826 a(n) = round((2*n+1)*(2*n^2 + 2*n + 27)/96).
%F A175826 a(n) = floor((n+1)*(2*n^2 + n + 27)/48).
%F A175826 a(n) = ceiling((2*n^3 + 3*n^2 + 28*n)/48).
%F A175826 a(n) = a(n-8) + (n+1)*(n-8) + 30.
%F A175826 From _R. J. Mathar_, Dec 06 2010: (Start)
%F A175826 G.f.: x*(1 - x + x^2 + x^4 - x^3) / ( (1+x)*(1+x^2)*(x-1)^4 ).
%F A175826 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-4) - 3*a(n-5) + 3*a(n-6) - a(n-7). (End)
%e A175826 a(8) = 0 + 1 + 1 + 2 + 2 + 4 + 5 + 7 + 8 = 30.
%p A175826 seq(floor((n+1)*(2*n^2+n+27)/48),n=0..50)
%o A175826 (Magma) [&+[Ceiling(k^2/8): k in [0..n]]: n in [0..50]];  // _Bruno Berselli_, Apr 26 2011
%o A175826 (PARI) a(n)=(n+1)*(2*n^2+n+27)\48 \\ _Charles R Greathouse IV_, Oct 19 2022
%Y A175826 Cf. A175822.
%K A175826 nonn,easy
%O A175826 0,3
%A A175826 _Mircea Merca_, Dec 05 2010