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A163440
Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
1
1, 15, 210, 2940, 41160, 576135, 8064420, 112881405, 1580053020, 22116729180, 309578036040, 4333306233165, 60655281460410, 849019887139515, 11884122064943310, 166347525415813560, 2328442863574420320
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170734, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
FORMULA
G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(91*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1).
a(n) = 13*a(n-1)+13*a(n-2)+13*a(n-3)+13*a(n-4)-91*a(n-5). - Wesley Ivan Hurt, May 10 2021
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^5)/(1-14*x+104*x^5-91*x^6), {x, 0, 30}], x] (* or *) LinearRecurrence[{13, 13, 13, 13, -91}, {15, 210, 2940, 41160, 576135}, 30] (* G. C. Greubel, Dec 23 2016 *)
coxG[{5, 91, -13}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 12 2019 *)
PROG
(PARI) my(x='x+O('x^30)); Vec((1+x)*(1-x^5)/(1-14*x+104*x^5-91*x^6)) \\ G. C. Greubel, Dec 23 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-14*x+104*x^5-91*x^6) )); // G. C. Greubel, May 12 2019
(Sage) ((1+x)*(1-x^5)/(1-14*x+104*x^5-91*x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 12 2019
CROSSREFS
Sequence in context: A162785 A076139 A163091 * A163962 A164626 A164860
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved