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A063808
Spherical growth series for Z as generated by {2, 3}.
1
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
0,2
COMMENTS
Decimal expansion of 223/1500. - Elmo R. Oliveira, May 05 2024
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).
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
MATHEMATICA
PadRight[{1, 4, 8}, 100, 6] (* Paolo Xausa, Nov 14 2023 *)
CROSSREFS
Cf. A308196 (partial sums).
Sequence in context: A177157 A081573 A201527 * A081455 A279160 A197290
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Aug 20 2001
STATUS
approved