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 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 (list; graph; refs; listen; history; text; internal format)
 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 Table of n, a(n) for n=0..36. Walter Parry, Growth series of some wreath products, Trans. Amer. Math. Soc., Vol. 331 (1992), No. 2, 751-759. Index entries for linear recurrences with constant coefficients, signature (1, 3, 0, -5, -3, 2, 3, 1). FORMULA G.f.: (1+x)(1-x^2)^2*(1+x+x^2)/((1-x^2-x^3)^2*(1-x-x^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 Sequence in context: A246597 A179906 A236913 * A018078 A005404 A249795 Adjacent sequences: A288345 A288346 A288347 * A288349 A288350 A288351 KEYWORD nonn AUTHOR Andrew Woods, Jun 08 2017 STATUS approved

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Last modified September 17 17:26 EDT 2024. Contains 375990 sequences. (Running on oeis4.)