A063808 Spherical growth series for Z as generated by {2, 3}.
1, 4, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6
Offset: 0
References
- P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 152.
- Avinoam Mann, How Groups Grow, London Mathematical Society Lecture Note Series, Vol. 335, Cambridge University Press, 2012; ISBN: 1107657504,9781107657502. See Example 6, page 3.
- P. Wagreich, The growth function of a discrete group (Lecture Notes in Mathematics, Vol. 956, Group Actions and Vector Fields, 1982, Vol. 956, pp. 125-144). Springer Berlin Heidelberg. See Example (3.2).
Links
- Index entries for linear recurrences with constant coefficients, signature (1).
Crossrefs
Cf. A308196 (partial sums).
Programs
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Mathematica
PadRight[{1,4,8},100,6] (* Paolo Xausa, Nov 14 2023 *)
Formula
G.f.: (1+3*x+4*x^2-2*x^3)/(1-x).
a(n) = 6 for n >= 3. - Elmo R. Oliveira, May 05 2024
E.g.f.: 6*exp(x) - 5 - 2*x + x^2. - Elmo R. Oliveira, Aug 09 2024
Comments