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A163601
Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
1
1, 36, 1260, 44100, 1543500, 54021870, 1890743400, 66175247880, 2316106686600, 81062789409000, 2837164567941270, 99299602743358500, 3475445596778953980, 121639178430430006500, 4257321634653990493500, 149004520868736130568670
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170755, 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)/(595*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).
a(n) = 34*a(n-1)+34*a(n-2)+34*a(n-3)+34*a(n-4)-595*a(n-5). - Wesley Ivan Hurt, May 11 2021
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^5)/(1-35*x+629*x^5-595*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 29 2017 *)
coxG[{5, 595, -34}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 22 2019 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-35*x+629*x^5-595*x^6)) \\ G. C. Greubel, Jul 29 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-35*x+629*x^5-595*x^6) )); // G. C. Greubel, May 22 2019
(Sage) ((1+x)*(1-x^4)/(1-35*x+629*x^5-595*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 22 2019
(GAP) a:=[36, 1260, 44100, 1543500, 54021870];; for n in [6..20] do a[n]:=34*(a[n-1]+a[n-2] +a[n-3]+a[n-4]) - 595*a[n-5]; od; Concatenation([1], a); # G. C. Greubel, May 22 2019
CROSSREFS
Sequence in context: A270961 A162850 A163219 * A164069 A164672 A165168
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved