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Partial sums of floor(n^2/10) (A056865)
0

%I #15 May 31 2012 19:36:23

%S 0,0,0,0,1,3,6,10,16,24,34,46,60,76,95,117,142,170,202,238,278,322,

%T 370,422,479,541,608,680,758,842,932,1028,1130,1238,1353,1475,1604,

%U 1740,1884,2036,2196,2364,2540,2724,2917,3119,3330,3550,3780

%N Partial sums of floor(n^2/10) (A056865)

%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) = sum(k=0..n,floor(k^2/10)).

%F a(n) = a(n-10)+(n-5)^2+n-1 , n>9.

%F G.f.: x^4*(1+x^4) / ( (1+x)*(x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1)*(x-1)^4 ). [R. J. Mathar, Nov 24 2010]

%F a(n)= +3*a(n-1) -3*a(n-2) +a(n-3) +a(n-10) -3*a(n-11) +3*a(n-12) -a(n-13). [R. J. Mathar, Nov 24 2010]

%e a(9) = 0+0+0+0+1+2+3+4+6+8 = 24

%t Accumulate[Floor[Range[0,50]^2/10]] (* _Harvey P. Dale_, May 31 2012 *)

%Y Cf. A056865

%K nonn

%O 0,6

%A _Mircea Merca_, Nov 24 2010