A359798
Cogrowth sequence of the group Z wr Z where wr denotes the wreath product.
Original entry on oeis.org
1, 4, 28, 232, 2108, 20384, 206392, 2165720, 23385340, 258532216, 2915343808, 33437862352, 389230520888, 4590271681064, 54767161155000, 660307913374352, 8036973478493436, 98672644594401736, 1221090110502080440, 15222093531642444504
Offset: 0
- Andrew Elvey Price, Table of n, a(n) for n = 0..500
- Andrew Elvey Price and A. J. Guttmann, Numerical studies of Thompson's group F and related groups, arXiv:1706.07571 [math.GR], 2017.
- C. Pittet and L. Saloff-Coste, On random walks on wreath products, The annals of probability, 30 No. 2 (2002), 948-977.
- Wikipedia, Wreath product
A294781
Growth of the Lamplighter group: number of elements in the Lamplighter group Z wr Z of length up to n with respect to the standard generating set {a,t}.
Original entry on oeis.org
1, 5, 17, 53, 153, 421, 1125, 2937, 7537, 19093, 47881, 119133, 294585, 724869, 1776717, 4341425, 10582177, 25743269, 62527553, 151682821, 367594457, 890137893, 2154129717, 5210373929, 12597758737, 30449544885, 73580024633, 177767884973, 429416696185, 1037172672005, 2504846014621
Offset: 0
a(2)=17, since the elements of length up to 2 are 1, a, a^-1, t, t^-1, a^2, at, at^-1, a^-2, a^-1t, a^-1t^-1, ta, ta^-1, t^2, t^-1a, t^-1a^-1, t^-2.
- Walter Parry, Growth series of some wreath products, Trans. Amer. Math. Soc. 331 (1992), 751-759.
- Index entries for linear recurrences with constant coefficients, signature (4, -2, -4, -4, 4, 6, 4, 1).
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CoefficientList[ Series[-((x^2 + 1) (x - 1)^2 (x + 1)^3)/((x^3 + x^2 + x - 1)^2 (x^2 + 2 x - 1)), {x, 0, 27}], x] (* or *)
LinearRecurrence[{4, -2, -4, -4, 4, 6, 4, 1}, {1, 5, 17, 53, 153, 421, 1125, 2937}, 28] (* Robert G. Wilson v, Aug 08 2018 *)
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