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A138585
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The sequence is formed by concatenating subsequences S1;S2;... each of finite length. S1 consists of the element 1. The n-th subsequence consist of numbers {(n/2)*(n/2 -1)+1 ; ... ; (n/2)*(n/2 +1)} for n even, {((n-1)/2)^2; ... ; (n-1)/2 * ((n-1)/2 +2)} for n odd.
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1
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1, 1, 2, 1, 2, 3, 3, 4, 5, 6, 4, 5, 6, 7, 8, 7, 8, 9, 10, 11, 12, 9, 10, 11, 12, 13, 14, 15, 13, 14, 15, 16, 17, 18, 19, 20, 16, 17, 18, 19, 20, 21, 22, 23, 24, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 31, 32, 33, 34, 35
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| A generalized Connell sequence.
Except for the first term the first element of each subsequence Sn (equivalently, each row of the triangle) gives A004652 (offset by 1), and the last element is A035106.
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LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 1..10000
Douglas E. Iannucci and Donna Mills-Taylor. On Generalizing the Connell Sequence. Journal of Integer Sequences 2 (1999), Article 99.1.7.
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EXAMPLE
| S1 : {1}
S2 : {1;2}
S3 : {1;2;3;}
S4 : {3;4;5;6}
S5 : {4;5;6;7;8}
S6 : {7;8;9;10;11;12} etc.
so concatenation of S1/S2/S3/S4/S5/S6... gives :
1;1;2;1;2;3;3;4;5;6;4;5;6;7;8;7;8;9;10;11;12;...
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MAPLE
| S := proc(n) local s: if(n=1)then s:=1: elif(n mod 2 = 0)then s:=(n/2)*(n/2 -1)+1: else s:=((n-1)/2)^2: fi: seq(k, k=s..s+n-1): end: seq(S(n), n=1..12); # Nathaniel Johnston, Oct 01 2011
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CROSSREFS
| Cf. A001614.
Sequence in context: A048219 A087188 A102885 * A070048 A116498 A143472
Adjacent sequences: A138582 A138583 A138584 * A138586 A138587 A138588
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KEYWORD
| easy,nonn
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AUTHOR
| Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), May 13 2008
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EXTENSIONS
| Corrected and edited by D. S. McNeil (mcneil(AT)hku.hk), Dec 12 2010
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