Search: id:A022554
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%I A022554
%S A022554 0,1,2,3,5,7,9,11,13,16,19,22,25,28,31,34,38,42,46,50,54,58,62,66,70,
%T A022554 75,80,85,90,95,100,105,110,115,120,125,131,137,143,149,155,161,167,
%U A022554 173,179,185,191,197,203,210,217,224,231,238,245,252,259,266,273,280
%N A022554 Sum [ sqrt(k) ], k=0..n.
%D A022554 D.E. Knuth, The art of programming, Vol. 1, 3rd Edition, Addison-Wesley, 
               1997, Ex. 43 of section 1.2.4.
%D A022554 M. Griffiths, More sums involving the floor function, Math. Gaz., 86 
               (2002), 285-287.
%F A022554 a(0)=0, a(1)=1; a(n) = 2 a(n-1) - a(n-2) if n is not a perfect square; 
               a(n) = 2 a(n-1) - a(n-2) + 1 if n is a perfect square.
%F A022554 a(n) = floor(sqrt(n)) * (n-1/6*(2*floor(sqrt(n))+5)*(floor(sqrt(n))-1)) 
               - Yong Kong (ykong(AT)curagen.com), Mar 10 2001
%p A022554 Sum(floor(sqrt(k)),k=0..n)
%Y A022554 Sequence in context: A129895 A096149 A033055 this_sequence A097046 A011861 
               A065520
%Y A022554 Adjacent sequences: A022551 A022552 A022553 this_sequence A022555 A022556 
               A022557
%K A022554 nonn,easy
%O A022554 0,3
%A A022554 Michel Tixier (tixier(AT)dyadel.net)
%E A022554 More terms from Yong Kong (ykong(AT)curagen.com), Mar 10 2001

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