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URL: https://oeis.org/A163645

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A163645
Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
1
1, 37, 1332, 47952, 1726272, 62145126, 2237200560, 80538357690, 2899349827920, 104375476044000, 3757476898626570, 135267719763613500, 4869585762918574950, 175303210136598476100, 6310847981816367469200
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170756, 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)/(630*t^5 - 35*t^4 - 35*t^3 - 35*t^2 - 35*t + 1).
a(n) = -630*a(n-5) + 35*Sum_{k=1..4} a(n-k). - Wesley Ivan Hurt, May 05 2021
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^5)/(1-36*x+665*x^5-630*x^6), {x, 0, 20}], x] (* G. C. Greubel, Aug 01 2017 *)
coxG[{5, 630, -35}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 31 2018 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-36*x+665*x^5-630*x^6)) \\ G. C. Greubel, Aug 01 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-36*x+665*x^5-630*x^6) )); // G. C. Greubel, May 22 2019
(SageMath) ((1+x)*(1-x^5)/(1-36*x+665*x^5-630*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 22 2019
(GAP) a:=[37, 1332, 47952, 1726272, 62145126];; for n in [6..20] do a[n]:=18*(a[n-1]+a[n-2] +a[n-3]+a[n-4] -18*a[n-5]); od; Concatenation([1], a); # G. C. Greubel, May 22 2019
CROSSREFS
Sequence in context: A219420 A162851 A163220 * A164070 A164673 A165169
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved