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Search: id:A039699
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| A039699 |
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Number of 4-dimensional cubic lattice walks that start and end at origin after 2n steps, free to pass through origin at intermediate stages. |
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1
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| 1, 8, 168, 5120, 190120, 7939008, 357713664, 16993726464, 839358285480, 42714450658880, 2225741588095168, 118227198981126144, 6380762273973278464, 349019710593278412800, 19310744204362333900800
(list; graph; listen)
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OFFSET
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0,2
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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, Symmetric Random Walk on n-Dimensional Integer Lattice
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FORMULA
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1, 0, 8, 0, 168, 0, 5120... has e.g.f.=BesselI[ 0, 2x ]^4 (BesselI=modified Bessel function of first kind).
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EXAMPLE
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a(5)=7939008 i.e. there are 7939008 different walks that start and end at origin of a 4-dimensional integer lattice after 2*5=10 steps, free to pass through origin at intermediate steps.
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CROSSREFS
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1-dimensional, 2-dimensional, 3-dimensional analogues are A000984, A002894, A002896 with e.g.f. (see above) = BesselI[ 0, 2x ]^1, BesselI[ 0, 2x ]^2, BesselI[ 0, 2x ]^3.
Sequence in context: A033454 A032395 A090228 this_sequence A084941 A139564 A001534
Adjacent sequences: A039696 A039697 A039698 this_sequence A039700 A039701 A039702
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KEYWORD
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nonn,nice,easy,walk
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AUTHOR
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Alessandro Zinani (alzinani(AT)tin.it)
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