%I A000194
%S A000194 1,1,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,
%T A000194 6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,
%U A000194 8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10
%N A000194 n appears 2n times; also nearest integer to square root of n.
%C A000194 a(n) = inverse (frequency distribution) sequence of A002378(n-1). [From 
               Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Jun 14 2009]
%D A000194 B. C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, see p. 
               78, Entry 24.
%D A000194 M. A. Nyblom, Some curious sequences ..., Am. Math. Monthly 109 (#6, 
               200), 559-564.
%D A000194 G. Gutin, Problem 913 (BCC20.5), Mediated digraphs, in Research Problems 
               from the 20th British Combinatorial Conference, Discrete Math., 308 
               (2008), 621-630.
%H A000194 T. D. Noe, <a href="b000194.txt">Table of n, a(n) for n=1..1000</a>
%H A000194 M. Somos, <a href="a073189.txt">Sequences used for indexing triangular 
               or square arrays</a>
%F A000194 G.f.: f(x^2, x^6)*x/(1-x) where f(a, b) is Ramanujan's theta function.
%F A000194 a(n)=a(n-2*a(n-a(n-1)))+1. - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Oct 27 2002
%F A000194 a(n+1)=a(n)+A005369(n).
%F A000194 a(n)=floor((1/2)*(1 + sqrt(4*n - 3))). - Zak Seidov, Jan 18 2006
%F A000194 a(n) = A000037(n) - n. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), 
               Jun 14 2009]
%p A000194 Digits := 100; f := n->round(evalf(sqrt(n))); [ seq(f(n), n=1..100) ];
%o A000194 (PARI) a(n)=if(n<0,0,ceil(sqrtint(4*n)/2)) - Michael Somos Feb 11 2004
%Y A000194 Partial sums of A005369.
%Y A000194 A000037(n) - n.
%Y A000194 Sequence in context: A023967 A090532 A003058 this_sequence A097429 A100617 
               A076471
%Y A000194 Adjacent sequences: A000191 A000192 A000193 this_sequence A000195 A000196 
               A000197
%K A000194 nonn,easy,nice
%O A000194 1,3
%A A000194 N. J. A. Sloane (njas(AT)research.att.com).
%E A000194 Additional comments from Michael Somos, May 31, 2000.