

A288348


Spherical growth function of the Lamplighter group L_2 with respect to the standard generators a, t.


3



1, 3, 6, 12, 22, 40, 71, 123, 212, 360, 607, 1017, 1693, 2807, 4635, 7629, 12524, 20512, 33532, 54728, 89201, 145223, 236200, 383858, 623393, 1011813, 1641441, 2661767, 4314821, 6992417, 11328796, 18350552, 29719248, 48124026, 77916923, 126140917, 204193454
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OFFSET

0,2


COMMENTS

Here t and t^{1} can be thought of as moves left and right, while a=a^{1} represents the lighting or extinguishing of a lamp.


LINKS



FORMULA

G.f.: (1+x)(1x^2)^2*(1+x+x^2)/((1x^2x^3)^2*(1xx^2)).


EXAMPLE

Writing L and R for t and t^{1}, there are 12 elements of the group which can be written as words of length 3, but not more briefly: LLL, LLa, LaL, LaR, aLL, aLa, aRa, aRR, RaL, RaR, RRa, and RRR.


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



