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A001614
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Connell sequence: 1 odd, 2 even, 3 odd, ...
(Formerly M0962 N0359)
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35
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1, 2, 4, 5, 7, 9, 10, 12, 14, 16, 17, 19, 21, 23, 25, 26, 28, 30, 32, 34, 36, 37, 39, 41, 43, 45, 47, 49, 50, 52, 54, 56, 58, 60, 62, 64, 65, 67, 69, 71, 73, 75, 77, 79, 81, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 122
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Next (2n-1) odd numbers alternating with next 2n even numbers. Squares (A000290(n)) occur at the A000217(n)-th entry. - Lekraj Beedassy (blekraj(AT)yahoo.com), Aug 06 2004. - Comment corrected by Daniel Forgues (squid(AT)zensearch.com), Jul 18 2009
a(t_n) = a(n(n+1)/2) = n^2 relates squares to triangular numbers. - Daniel Forgues
The natural numbers not included are A118011(n) = 4n - a(n) as n=1,2,3,... - Paul D. Hanna (pauldhanna(AT)juno.com), Apr 10 2006
As a triangle with row sums = A069778: (1, 6, 21, 52, 105,...):/Q 1;/Q 2, 4;/Q 5, 7, 9;/Q 10, 12, 14, 16;/Q ... [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 01 2008]
The triangle sums, see A180662 for their definitions, link the Connell sequence A001614 as a triangle with six sequences, see the crossrefs. [From Johannes W. Meijer, May 20 2011]
a(n) = A122797(n) + n - 1. [Reinhard Zumkeller, Feb 12 2012]
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REFERENCES
| C. Pickover, Computers and the Imagination, St. Martin's Press, NY, 1991, p. 276.
C. A. Pickover, The Mathematics of Oz, Chapter 39, Camb. Univ. Press UK 2002.
Problem E1382, Amer. Math. Monthly, 67 (1960), 380.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
Douglas E. Iannucci and Donna Mills-Taylor, On Generalizing the Connell Sequence, J. Integer Sequences, Vol. 2, 1999, #99.1.7.
Gary E. Stevens, A Connell-Like Sequence, J. Integer Sequences, Vol. 1, 1998, #98.1.4.
Eric Weisstein's World of Mathematics, Connell Sequence
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FORMULA
| a(n) = 2*n - floor( (1+ sqrt(8*n-7))/2 ).
a(n)=A005843(n) - A002024(n). - Lekraj Beedassy (blekraj(AT)yahoo.com), Aug 06 2004
a(n) = A118012(A118011(n)). A117384( a(n) ) = n; A117384( 4*n - a(n) ) = n. - Paul D. Hanna (pauldhanna(AT)juno.com), Apr 10 2006
a(1)=1; then a(n)=a(n-1)+1 if a(n-1) is a square, a(n)=a(n-1)+2 otherwise. For example, a(21)=36 is a square therefore a(22)=36+1=37 which is not a square so a(23)=37+2=39 ... - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 07 2007
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MAPLE
| A001614:=proc(n): 2*n - floor((1+sqrt(8*n-7))/2) end: seq(A001614(n), n=1..67); [From Johannes W. Meijer, May 20 2011]
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MATHEMATICA
| lst={}; i=0; For[j=1, j<=4!, a=i+1; b=j; k=0; For[i=a, i<=9!, k++; AppendTo[lst, i]; If[k>=b, Break[]]; i=i+2]; j++ ]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 29 2008]
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PROG
| (Haskell)
a001614 n = a001614_list !! (n-1)
a001614_list = f 0 0 a057211_list where
f c z (x:xs) = z' : f x z' xs where z' = z + 1 + 0 ^ abs (x - c)
-- Reinhard Zumkeller, Dec 30 2011
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CROSSREFS
| Cf. A117384, A118011 (complement), A118012.
A069778 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 01 2008]
From Johannes W. Meijer, May 20 2011: (Start)
Triangle columns: A002522, A117950 (n>=1), A117951 (n>=2), A117619 (n>=3), A154533 (n>=5), A000290 (n>=1), A008865 (n>=2), A028347 (n>=3), A028878 (n>=1), A028884 (n>=2), A054569 [T(2*n,n)].
Triangle sums (see the comments): A069778 (Row1), A190716 (Row2), A058187 (Related to Kn11, Kn12, Kn13, Kn21, Kn22, Kn23, Fi1, Fi2, Ze1 and Ze2), A000292 (Related to Kn3, Kn4, Ca3, Ca4, Gi3 and Gi4), A190717 (Related to Ca1, Ca2, Ze3, Ze4), A190718 (Related to Gi1 and Gi2). (End)
Cf. A057211.
Sequence in context: A106829 A190228 A083120 * A050731 A098794 A114055
Adjacent sequences: A001611 A001612 A001613 * A001615 A001616 A001617
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KEYWORD
| nonn,easy,nice,tabl,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Mar 16 2001
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