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Search: id:A051437
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| A051437 |
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Undirected walks of length n+1 on an oriented triangle, visiting n+2 vertices, with n "corners"; the symmetry group is C3. Walks are not self-avoiding. |
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+0
2
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| 1, 3, 4, 10, 16, 36, 64, 136, 256, 528, 1024, 2080, 4096, 8256, 16384, 32896, 65536, 131328, 262144, 524800, 1048576, 2098176, 4194304, 8390656, 16777216, 33558528
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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n=2m: a(n)=2^(n-1)+2^((n-2)/2); n=2m+1: a(n)=2^(n-1).
Binomial transform is 3^n+Pell(n) (A000244(n)+A000129(n)). G.f. : (1+x-4x^2)/((1-2x)(1-2x^2)); a(n)=2^n+2^(n/2)(1-(-1)^n)/(2sqrt(2)). - Paul Barry (pbarry(AT)wit.ie), Apr 28 2004
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EXAMPLE
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For n=3 the walks visit vertices 1212, 1213, 1232, 1231.
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CROSSREFS
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Cf. A005418.
Adjacent sequences: A051434 A051435 A051436 this_sequence A051438 A051439 A051440
Sequence in context: A037952 A093512 A081160 this_sequence A034774 A144958 A034775
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KEYWORD
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nonn,nice,easy
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AUTHOR
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Colin Mallows colinm(AT)research.avayalabs.com
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