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A163600
Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
1
1, 35, 1190, 40460, 1375640, 46771165, 1590199380, 54066091695, 1838223751980, 62498813135220, 2124932636259510, 72246791293015185, 2456359680805901640, 83515167573569420535, 2839479604449882838290, 96541079403144247211340
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170754, 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)/(561*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).
a(n) = 33*a(n-1)+33*a(n-2)+33*a(n-3)+33*a(n-4)-561*a(n-5). - Wesley Ivan Hurt, May 11 2021
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^5)/(1-34*x+594*x^5-561*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 29 2017 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-34*x+594*x^5-561*x^6)) \\ G. C. Greubel, Jul 29 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-34*x+594*x^5-561*x^6) )); // G. C. Greubel, Apr 28 2019
(Sage) ((1+x)*(1-x^5)/(1-34*x+594*x^5-561*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019
CROSSREFS
Sequence in context: A029546 A305539 A163218 * A164068 A164671 A165167
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved