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A167092
Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.
1
1, 39, 1482, 56316, 2140008, 81320304, 3090171552, 117426518976, 4462207721088, 169563893401344, 6443427949251072, 244850262071540736, 9304309958718547968, 353563778431304822043, 13435423580389583209476
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170758, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
Index entries for linear recurrences with constant coefficients, signature (37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, -703).
FORMULA
G.f.: (t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(703*t^13 - 37*t^12 - 37*t^11 - 37*t^10 - 37*t^9 - 37*t^8 - 37*t^7 - 37*t^6 - 37*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1).
MATHEMATICA
CoefficientList[Series[(t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(703*t^13 - 37*t^12 - 37*t^11 - 37*t^10 - 37*t^9 - 37*t^8 - 37*t^7 - 37*t^6 - 37*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Jun 02 2016 *)
coxG[{13, 703, -37}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 21 2022 *)
CROSSREFS
Sequence in context: A166171 A166433 A166691 * A167537 A167828 A167955
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved