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A360715
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Number of self-avoiding paths with nodes chosen among n given points on a circle; one-node paths are allowed.
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2
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1, 3, 9, 30, 105, 369, 1281, 4380, 14769, 49215, 162393, 531450, 1727193, 5580141, 17936145, 57395640, 182948577, 581130747, 1840247337, 5811307350, 18305618121, 57531942633, 180441092769, 564859072980, 1765184603025, 5507375961399, 17157594341241, 53379182394930, 165856745298489, 514727830236645
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = (n/4)*(3^(n-1)+3).
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EXAMPLE
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a(4) = A001792(2) + 4*A001792(1) + 6 + 4 = 8 + 4*3 + 6 + 4 = 30 with the four summands corresponding to paths with 4, 3, 2 and 1 nodes, respectively.
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CROSSREFS
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If one-node paths are not allowed, one gets A261064. Cf. A001792 if all n points need to be used.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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