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A163218
Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
1
1, 35, 1190, 40460, 1375045, 46731300, 1588176975, 53974651500, 1834344072330, 62340711467265, 2118667029023160, 72003509011079415, 2447059985777227590, 83164038200838759780, 2826353783752411211145, 96054447135432681999180
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^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(561*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).
a(n) = -561*a(n-4) + 33*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)/(561*t^4-33*t^3-33*t^2 - 33*t+1), {t, 0, 20}], t] (* or *) LinearRecurrence[{33, 33, 33, -561}, {1, 35, 1190, 40460}, 20] (* G. C. Greubel, Dec 11 2016 *)
coxG[{4, 561, -33}] (* 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)/(561*t^4-33*t^3 - 33*t^2-33*t+1)) \\ G. C. Greubel, Dec 11 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-34*x+594*x^4-x^561*x^5) )); // G. C. Greubel, Apr 30 2019
(Sage) ((1+x)*(1-x^4)/(1-34*x+594*x^4-561*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 30 2019
CROSSREFS
Sequence in context: A162847 A029546 A305539 * A163600 A164068 A164671
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved