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Search: id:A056023
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| A056023 |
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Unique triangle such that (1) every positive integer occurs exactly once; (2) row n consists of n consecutive numbers; (3) odd-numbered rows are decreasing; and (4) even-numbered rows are increasing. |
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+0
2
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| 1, 2, 3, 6, 5, 4, 7, 8, 9, 10, 15, 14, 13, 12, 11, 16, 17, 18, 19, 20, 21, 28, 27, 26, 25, 24, 23, 22, 29, 30, 31, 32, 33, 34, 35, 36, 45, 44, 43, 42, 41, 40, 39, 38, 37, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Self-inverse permutation of the natural numbers.
T(2*n-1,1)=A000217(2*n-1)=T(2*n,1)-1; T(2*n,4*n)=A000217(2*n)=T(2*n+1,4*n+1)-1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 25 2004
Mirror image of triangle in A056011 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 04 2009]
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LINKS
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Index entries for sequences that are permutations of the natural numbers
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FORMULA
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T(n, k) = (n^2 - (n - 2*k)*(-1)^(n mod 2)) / 2 + n mod 2. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 25 2004
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EXAMPLE
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Triangle begins : 1 ; 2,3 ; 6,5,4 ; 7,8,9,10 ; 15,14,13,12,11 ; ... [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 04 2009]
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CROSSREFS
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Cf. A056011 [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 04 2009]
Sequence in context: A091556 A072298 A130686 this_sequence A133259 A120067 A089843
Adjacent sequences: A056020 A056021 A056022 this_sequence A056024 A056025 A056026
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Aug 01 2000.
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