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A359797
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Cogrowth sequence of the lamplighter group Z_2 wr Z where wr denotes the wreath product.
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2
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1, 3, 15, 87, 547, 3623, 24885, 175591, 1265187, 9271167, 68894785, 518053231, 3935274277, 30158804835, 232930956175, 1811476156847, 14174669041427, 111532445963367, 882004732285473, 7006931317108119, 55899039962599777, 447666261592033123
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OFFSET
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0,2
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COMMENTS
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a(n) is the number of words of length 2n in the letters a,t,t^(-1) that equal the identity of the lamplighter group Z_2 wr Z = <a,t | a^2=1, [a,t^(-k)at^k]=1 for all k >.
Walks on this group can be seen as operations on an infinite tape of 0's and 1's where each step is either a right shift, left shift or toggles the current element. a(n) is then the number of sequences of 2n such moves which return the tape to the initial position.
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LINKS
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CROSSREFS
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Spherical growth sequence for this group is A288348.
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KEYWORD
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nonn,walk
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AUTHOR
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STATUS
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approved
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