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A229644 Cogrowth function of the group Baumslag-Solitar(2,2). 10
1, 4, 28, 244, 2396, 25324, 281140, 3232352, 38151196, 459594316, 5628197948, 69859456440, 876985904276, 11115789165888, 142066687799680, 1828884017527504, 23694360858872604, 308714491495346028, 4042605442981407388, 53178663502737007352 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is the number of words of length 2n in the letters a,a^{-1},t,t^{-1} that equal the identity of the group BS(2,2)=<a,t | ta^2=a^2t>.

LINKS

Murray Elder, Table of n, a(n) for n = 0..50

M. Elder, A. Rechnitzer, E. J. Janse van Rensburg, T. Wong, The cogrowth series for BS(N,N) is D-finite

Wikipedia, Baumslag-Solitar group

Index entries for sequences related to groups

EXAMPLE

For n=1 there are 4 words of length 2 equal to the identity: aa^{-1}, a^{-1}a, tt^{-1}, t^{-1}t.

CROSSREFS

The cogrowth sequences for BS(N,N) for N = 1..10 are A002894, A229644, A229645, A229646, A229647, A229648, A229649, A229650, A229651, A229652.

Sequence in context: A192625 A199561 A103211 * A228714 A230640 A300050

Adjacent sequences:  A229641 A229642 A229643 * A229645 A229646 A229647

KEYWORD

nonn,walk

AUTHOR

Murray Elder, Sep 27 2013

STATUS

approved

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Last modified October 27 23:46 EDT 2021. Contains 348305 sequences. (Running on oeis4.)