login
A163454
Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
1
1, 20, 380, 7220, 137180, 2606230, 49514760, 940712040, 17872229160, 339547661640, 6450936451470, 122558879953620, 2328449391567180, 44237321450224020, 840447989197392780, 15967350630411275430
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170739, 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)/(171*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1).
a(n) = 18*a(n-1)+18*a(n-2)+18*a(n-3)+18*a(n-4)-171*a(n-5). - Wesley Ivan Hurt, May 10 2021
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^5)/(1-19*x+189*x^5-171*x^6), {x, 0, 20}], x] (* or *) LinearRecurrence[{18, 18, 18, 18, -171}, {1, 20, 380, 7220, 137180, 2606230}, 20] (* G. C. Greubel, Dec 24 2016 *)
coxG[{5, 171, -18}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 13 2019 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-19*x+189*x^5-171*x^6)) \\ G. C. Greubel, Dec 24 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-19*x+189*x^5-171*x^6) )); // G. C. Greubel, May 13 2019
(Sage) ((1+x)*(1-x^5)/(1-19*x+189*x^5-171*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 13 2019
CROSSREFS
Sequence in context: A097832 A342886 A163124 * A163969 A164633 A164911
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved