login
A163220
Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
1
1, 37, 1332, 47952, 1725606, 62097840, 2234659770, 80416702800, 2893883982570, 104139615440700, 3747579228757350, 134860782963557700, 4853114416362432150, 174644689291688511000, 6284782282271390399250
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^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(630*t^4 - 35*t^3 - 35*t^2 - 35*t + 1).
a(n) = -630*a(n-4) + 35*Sum_{k=1..3} a(n-k). - Wesley Ivan Hurt, May 05 2021
MATHEMATICA
CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(630*t^4-35*t^3-35*t^2 - 35*t+1), {t, 0, 20}], t] (* or *) LinearRecurrence[{35, 35, 35, -630}, {1, 37, 1332, 47952}, 20] (* G. C. Greubel, Dec 11 2016 *)
coxG[{4, 630, -35}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 30 2019 *)
PROG
(PARI) my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(630*t^4-35*t^3 - 35*t^2-35*t+1)) \\ G. C. Greubel, Dec 11 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-36*x+665*x^4-630*x^5) )); // G. C. Greubel, Apr 30 2019
(Sage) ((1+x)*(1-x^4)/(1-36*x+665*x^4-630*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 30 2019
CROSSREFS
Sequence in context: A006062 A219420 A162851 * A163645 A164070 A164673
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved