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A000194
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n appears 2n times; also nearest integer to square root of n.
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24
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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, 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, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(n) = inverse (frequency distribution) sequence of A002378(n-1). [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Jun 14 2009]
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REFERENCES
| B. C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, see p. 78, Entry 24.
M. A. Nyblom, Some curious sequences ..., Am. Math. Monthly 109 (#6, 200), 559-564.
G. Gutin, Problem 913 (BCC20.5), Mediated digraphs, in Research Problems from the 20th British Combinatorial Conference, Discrete Math., 308 (2008), 621-630.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
M. Somos, Sequences used for indexing triangular or square arrays
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FORMULA
| G.f.: f(x^2, x^6)*x/(1-x) where f(a, b) is Ramanujan's theta function.
a(n)=a(n-2*a(n-a(n-1)))+1. - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 27 2002
a(n+1)=a(n)+A005369(n).
a(n)=floor((1/2)*(1 + sqrt(4*n - 3))). - Zak Seidov, Jan 18 2006
a(n) = A000037(n) - n. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Jun 14 2009]
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MAPLE
| Digits := 100; f := n->round(evalf(sqrt(n))); [ seq(f(n), n=1..100) ];
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MATHEMATICA
| A000194[n_] := Floor[(1 + Sqrt[4 n - 3])/2]; [From E. Perez Herrero (psychgeometry(AT)gmail.com), Apr 14 2010]
Flatten[Table[PadRight[{}, 2n, n], {n, 10}]] (* From Harvey P. Dale, Nov 16 2011 *)
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PROG
| (PARI) a(n)=if(n<0, 0, ceil(sqrtint(4*n)/2)) - Michael Somos Feb 11 2004
(Haskell)
a000194 n = a000194_list !! (n-1)
a000194_list = concat $ zipWith ($) (map replicate [2, 4..]) [1..]
-- Reinhard Zumkeller, Mar 18 2011
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CROSSREFS
| Partial sums of A005369.
A000037(n) - n.
Cf. A002024.
Sequence in context: A023967 A090532 A003058 * A168255 A097429 A100617
Adjacent sequences: A000191 A000192 A000193 * A000195 A000196 A000197
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Additional comments from Michael Somos, May 31, 2000.
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