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A163315 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I. 1
1, 4, 12, 36, 108, 318, 936, 2760, 8136, 23976, 70662, 208260, 613788, 1808964, 5331420, 15712878, 46309320, 136483800, 402247944, 1185513624, 3493970742, 10297504260, 30349021740, 89445276900, 263615006412, 776931706398 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A003946, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2, 2, 2, 2, -3).

FORMULA

G.f. (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(3*t^5 - 2*t^4 - 2*t^3 - 2*t^2 - 2*t + 1).

MATHEMATICA

CoefficientList[Series[(t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(3*t^5 - 2*t^4 - 2*t^3 - 2*t^2 - 2*t + 1), {t, 0, 50}], t] (* or *) Join[{1}, LinearRecurrence[{2, 2, 2, 2, -3}, {4, 12, 36, 108, 318}, 50]] (* G. C. Greubel, Dec 18 2016 *)

PROG

(PARI) Vec((t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(3*t^5 - 2*t^4 - 2*t^3 - 2*t^2 - 2*t + 1) +O(t^50)) \\ G. C. Greubel, Dec 18 2016

CROSSREFS

Sequence in context: A003212 A156945 A006817 * A003119 A001394 A156946

Adjacent sequences:  A163312 A163313 A163314 * A163316 A163317 A163318

KEYWORD

nonn,easy

AUTHOR

John Cannon and N. J. A. Sloane, Dec 03 2009

STATUS

approved

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Last modified February 21 01:12 EST 2019. Contains 320364 sequences. (Running on oeis4.)