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Search: id:A063888
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| A063888 |
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Number of n-step walks on a cube lattice starting from the origin but not returning to it at any stage. |
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+0
1
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| 1, 6, 30, 180, 1026, 6156, 35940, 215640, 1271106, 7626636, 45182124, 271092744, 1610875836, 9665255016, 57546367704, 345278206224, 2058613385346, 12351680312076, 73717606430364, 442305638582184, 2641804748619732
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OFFSET
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0,2
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COMMENT
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a(n)/6^n tends to 0.65946...
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 322-331.
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LINKS
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S. R. Finch, Polya's Random Walk Constants
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FORMULA
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a(2n) = 6*a(2n-1)-A049037(n); a(2n+1) = 6*a(2n).
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EXAMPLE
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a(2) = 30 since there are 36 2-step walks but 6 of them involve a return to the origin at some stage; similarly a(3) = 180 since there are 216 3-step walks but 36 of them involve a return to the origin at some stage.
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CROSSREFS
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Sequence in context: A089896 A057754 A001473 this_sequence A029571 A109501 A147517
Adjacent sequences: A063885 A063886 A063887 this_sequence A063889 A063890 A063891
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Aug 28 2001
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