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Cogrowth function of the group Baumslag-Solitar(10,10).
10

%I #10 Oct 22 2015 14:49:00

%S 1,4,28,232,2092,19864,195352,1970896,20275660,211823800,2240795848,

%T 23951289564,258255473032,2805534386256,30675481454184,

%U 337306578693652,3727580774618060,41376921517941032,461122691909043112,5157400529078643552

%N Cogrowth function of the group Baumslag-Solitar(10,10).

%C 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(10,10)=<a,t | ta^{10}=a^{10}t>.

%H Murray Elder, <a href="/A229652/b229652.txt">Table of n, a(n) for n = 0..50</a>

%H M. Elder, A. Rechnitzer, E. J. Janse van Rensburg, T. Wong, <a href="http://arxiv.org/abs/1309.4184">The cogrowth series for BS(N,N) is D-finite</a>

%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>

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

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

%K nonn,walk

%O 0,2

%A _Murray Elder_, Sep 28 2013