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A164001
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Spiral of triangles around a hexagon.
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9
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1, 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
(list;
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refs;
listen;
history;
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OFFSET
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1,2
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COMMENTS
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a(n) is the side length of the n-th triangle in a spiral around a hexagon with side length = 1.
Sequence very similar to A134816, but without repeated terms. Records in A134816. Also records in A000931, the Padovan sequence.
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LINKS
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Table of n, a(n) for n=1..44.
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FORMULA
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If n<5 then a(n)=n otherwise a(n)=a(n-2)+a(n-3).
G.f.: -x-1+(-x^2-2*x-1)/(-1+x^2+x^3). a(n) = A000931(n+4) + A000931(n+5) = A000931(n+7), n>1. [From R. J. Mathar, Oct 29 2009]
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CROSSREFS
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The following are basically all variants of the same sequence: A000931, A078027, A096231, A124745, A133034, A134816, A164001, A182097 and probably A020720. However, each one has its own special features and deserves its own entry.
Sequence in context: A039877 A192433 A189083 * A117598 A120149 A117597
Adjacent sequences: A163998 A163999 A164000 * A164002 A164003 A164004
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KEYWORD
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easy,nonn
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AUTHOR
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Omar E. Pol, Oct 27 2009
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STATUS
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approved
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