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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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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
| B. Cloitre, On parity properties of certain Beatty sequences, in preparation 2004
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,1000
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FORMULA
| a(n)=3*n*(4*n+1)=3*A007742(n).
a(n)=24*n+a(n-1)-9 (with a(0)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
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EXAMPLE
| 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
a(1)=24*1+0-9=15; a(2)=24*2+15-9=54; a(3)=24*3+54-9=117 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
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PROG
| (PARI) { for (n=0, 1000, write("b063436.txt", n, " ", n*(12*n + 3)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 21 2009]
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CROSSREFS
| Cf. A062783, A000567.
Sequence in context: A193608 A194454 A198955 * A010004 A172073 A059145
Adjacent sequences: A063433 A063434 A063435 * A063437 A063438 A063439
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KEYWORD
| easy,nonn
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AUTHOR
| Floor van Lamoen (fvlamoen(AT)hotmail.com), Jul 21 2001
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