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Search: id:A063436
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| A063436 |
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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 upward direction. |
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+0
2
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| 0, 15, 54, 117, 204, 315, 450, 609, 792, 999, 1230, 1485, 1764, 2067, 2394, 2745, 3120, 3519, 3942, 4389, 4860, 5355, 5874, 6417, 6984, 7575, 8190, 8829, 9492, 10179, 10890, 11625, 12384, 13167, 13974, 14805, 15660, 16539, 17442, 18369
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Related to parity of Beatty sequences for exp(-(1/2)/n). Let f(k,n)=-sum(i=1,n,sum(j=1,i,(-1)^floor(j*exp(-(1/2)/n)))), then a(n)=Max{f(k,n) : 1<=k<=4*a(n)-2} and for 0<=i<=4*a(n)-3, f(i,n)=f(4*a(n)-2-i,n). - Benoit Cloitre (benoit7848c(AT)orange.fr), May 26 2004
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REFERENCES
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B. Cloitre, On parity properties of certain Beatty sequences, in preparation 2004
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FORMULA
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a(n)=3*n*(4*n+1)=3*A007742(n).
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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
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CROSSREFS
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Cf. A062783, A000567.
Sequence in context: A009962 A118238 A015234 this_sequence A010004 A059145 A086643
Adjacent sequences: A063433 A063434 A063435 this_sequence A063437 A063438 A063439
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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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