A229644 Cogrowth function of the group Baumslag-Solitar(2,2).

1, 4, 28, 244, 2396, 25324, 281140, 3232352, 38151196, 459594316, 5628197948, 69859456440, 876985904276, 11115789165888, 142066687799680, 1828884017527504, 23694360858872604, 308714491495346028, 4042605442981407388, 53178663502737007352

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 * A354602 A228714 A371693

Adjacent sequences: A229641 A229642 A229643 * A229645 A229646 A229647

Keyword

nonn,walk

Author

Murray Elder, Sep 27 2013

Status

approved