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%I #20 Sep 08 2022 08:45:51
%S 0,0,0,0,0,1,2,4,6,9,13,18,24,31,39,48,58,70,83,98,114,132,152,174,
%T 198,224,252,282,314,349,386,426,468,513,561,612,666,723,783,846,912,
%U 982,1055,1132,1212,1296,1384,1476,1572,1672,1776
%N Partial sums of floor(n^2/24).
%H Vincenzo Librandi, <a href="/A175780/b175780.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.
%F a(n) = round((2*n+1)*(2*n^2 + 2*n - 37)/288).
%F a(n) = floor((2*n+11)*(n-2)^2/144).
%F a(n) = ceiling((2*n-9)*(n+3)^2/144).
%F a(n) = a(n-24) + (n+1)*(n-24) + 198, n > 23.
%F G.f.: x^5*(1 - x + x^2 - x^3 + x^4) / ( (1+x)*(1+x^2)*(x^4-x^2+1)*(x^2-x+1)*(1+x+x^2)*(x-1)^4 ). - _R. J. Mathar_, Dec 06 2010
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-12) - 3*a(n-13) + 3*a(n-14) - a(n-15). - _R. J. Mathar_, Dec 06 2010
%e a(24) = 0 + 0 + 0 + 0 + 0 + 1 + 1 + 2 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 12 + 13 + 15 + 16 + 18 + 20 + 22 + 24 = 198.
%p seq(ceil((2*n-9)*(n+3)^2/144),n=0..50)
%o (Magma) [Round((2*n+1)*(2*n^2+2*n-37)/288): n in [0..60]]; // _Vincenzo Librandi_, Jun 22 2011
%Y Cf. A175777.
%K nonn,easy
%O 0,7
%A _Mircea Merca_, Dec 04 2010