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Search: id:A062783
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| 0, 9, 42, 99, 180, 285, 414, 567, 744, 945, 1170, 1419, 1692, 1989, 2310, 2655, 3024, 3417, 3834, 4275, 4740, 5229, 5742, 6279, 6840, 7425, 8034, 8667, 9324, 10005, 10710, 11439, 12192, 12969, 13770, 14595, 15444, 16317, 17214, 18135, 19080
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Write 1,2,3,4,... counterclockwise in a hexagonal spiral around 0 starting left down, then a(n) is the sequence found by reading from 0 in the vertical downward direction.
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REFERENCES
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L. Berzolari, Allgemeine Theorie der Ho"heren Ebenen Algebraischen Kurven, Encyclopa"die der Mathematischen Wissenschaften mit Einschluss ihrer Anwendungen. Band III_2. Heft 3, Leipzig: B.G. Teubner, 1906. p. 341.
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FORMULA
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a(n)=24*n+a(n-1)-39 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 14 2009]
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EXAMPLE
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The spiral begins:
......16..15..14
....17..5...4...13
..18..6...0...3...12
19..7...1...2...11..26
..20..8...9...10..25
....21..22..23..24
For n=2, a(2)=24*2+0-39=9; n=3, a(3)=24*3+9-39=42; n=4, a(4)=24*4+42-39=99 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 14 2009]
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MATHEMATICA
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s=0; lst={s}; Do[s+=n++ +9; AppendTo[lst, s], {n, 0, 8!, 24}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 17 2008]
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CROSSREFS
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Cf. A063436, A000567. Equals 3*A033991(n).
Sequence in context: A065792 A118546 A075233 this_sequence A027441 A000971 A061927
Adjacent sequences: A062780 A062781 A062782 this_sequence A062784 A062785 A062786
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KEYWORD
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easy,nonn
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AUTHOR
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Floor van Lamoen (fvlamoen(AT)hotmail.com), Jul 21 2001
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