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A063810 Growth series for Heisenberg group. 0
1, 4, 12, 36, 82, 164, 294, 476, 724, 1052, 1464, 1972, 2590, 3324, 4186, 5188, 6336, 7644, 9124, 10780, 12626, 14676, 16934, 19412, 22124, 25076, 28280, 31748, 35486, 39508, 43826, 48444, 53376, 58636, 64228, 70164, 76458, 83116 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 156.

LINKS

Table of n, a(n) for n=0..37.

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

Sequence in context: A020875 A307182 A190072 * A183931 A320967 A261584

Adjacent sequences:  A063807 A063808 A063809 * A063811 A063812 A063813

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Aug 20 2001

STATUS

approved

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Last modified July 26 16:44 EDT 2021. Contains 346294 sequences. (Running on oeis4.)