Search: id:A076644
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%I A076644
%S A076644 1,3,6,7,11,13,18,21,22,28,32,34,41,46,49,50,58,64,68,70,79,86,91,94,
%T A076644 95,105,113,119,123,125,136,145,152,157,160,161,173,183,191,197,201,
%U A076644 203,216,227,236,243,248,251,252,266,278,288,296,302,306,308,323,336
%N A076644 a(1)=1; for n>1, a(n) = a(n-floor(sqrt(n))) + n.
%C A076644 a(n) = floor(2/3*n*(sqrt(n)+1)) for n=1,2,4,6,17,24,26,29,43,83,88,193,
               207,243,357,534,806,1082,1197,1377... Sign of a(n) - floor(2/3*n*(sqrt(n)+1)) 
               changes often.
%C A076644 Cumulative sums of A122196. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), 
               Aug 25 2006
%F A076644 Write n=r^2+s with -r < s <= r; then a(n) = r(r+1)(4r-1)/6 + x, where 
               x = -s^2 if s <= 0, x = s(2r+1-s) if s >= 0. - Dean Hickerson (dean.hickerson(AT)yahoo.com), 
               Nov 11 2002
%F A076644 a(n) is asymptotic to 2/3*n^(3/2).
%t A076644 a[n_] := Module[{r, s}, r=Floor[1/2+Sqrt[n]]; s=n-r^2; (r(r+1)(4r-1))/
               6+If[s<=0, -s^2, s(2r+1-s)]]
%o A076644 (PARI) a(n)=if(n<2,n>0,n+a(n-sqrtint(n)))
%Y A076644 Cf. A122196.
%Y A076644 Sequence in context: A120511 A022550 A153033 this_sequence A087642 A084349 
               A126003
%Y A076644 Adjacent sequences: A076641 A076642 A076643 this_sequence A076645 A076646 
               A076647
%K A076644 nonn
%O A076644 1,2
%A A076644 Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 23 2002

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