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Search: id:A134816
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| A134816 |
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Padovan's spiral numbers. |
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+0
5
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| 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, 351, 465, 616, 816, 1081, 1432, 1897, 2513, 3329, 4410, 5842, 7739, 10252, 13581, 17991, 23833, 31572, 41824, 55405, 73396, 97229, 128801, 170625, 226030, 299426, 396655
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Numbers that are the side lengths of the equilateral triangles needed to draw the spiral which follow the Padovan sequence. This sequence appears to be essentially identical to one or more sequences already in the OEIS. See: A000931, A078027, A124745, A133034.
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FORMULA
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a(n)=A000931(n+4).
a(n)=Sum_{x=1..nth number of Padovan sequence}x [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru], 17 Jul 2009)
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EXAMPLE
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a(6)=3 because 6+4=10 and A000931(10)=3.
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MATHEMATICA
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Drop[ CoefficientList[ Series[(1 - x^2)/(1 - x^2 - x^3), {x, 0, 52}], x], 5] (* Or *) a[1] = a[2] = a[3] = 1; a[n_] := a[n] = a[n - 2] + a[n - 3]; Array[ a, 48] [From Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 30 2009]
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CROSSREFS
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Sequence in context: A133034 A000931 A078027 this_sequence A072493 A064324 A032277
Adjacent sequences: A134813 A134814 A134815 this_sequence A134817 A134818 A134819
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KEYWORD
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easy,nonn
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AUTHOR
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Omar E. Pol (info(AT)polprimos.com), Nov 13 2007
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 30 2009
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