OFFSET
0,2
REFERENCES
P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 156.
LINKS
Moon Duchin, Counting in Groups: Fine Asymptotic Geometry, Notices of the AMS 63.8 (2016), pp. 871-974. See p. 873. [There may be a typo for c_8 in the recurrence given there]
Moon Duchin and Michael Shapiro, Rational growth in the Heisenberg group, arXiv:1411.4201 [math.GR], 2014; see Section 11.4.2. [There may be a typo in the recurrence given there]
Index entries for linear recurrences with constant coefficients, signature (3,-4,5,-6,5,-4,3,-1)
FORMULA
G.f.: (1 + x + 4*x^2 + 11*x^3 + 8*x^4 + 21*x^5 + 6*x^6 + 9*x^7 + x^8)/((1-x)^4*(1+x+x^2)*(1+x^2)).
a(n) = (c_n + 31*n^3 - 57*n^2 + 105*n)/18 where c_n = -7, -14, 9, -16, -23, 18, -7, -32, 9, 2, -23, 0 for n >= 1, c_{n+12} = c_n. - R. J. Mathar, Sep 27 2016
MATHEMATICA
LinearRecurrence[{3, -4, 5, -6, 5, -4, 3, -1}, {1, 4, 12, 36, 82, 164, 294, 476, 724}, 40] (* Harvey P. Dale, Sep 02 2018 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Aug 20 2001
STATUS
approved