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A163207
Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
1
1, 29, 812, 22736, 636202, 17802288, 498146166, 13939191504, 390048294510, 10914382803996, 305407698579522, 8545958486918244, 239134137088822794, 6691482951706744632, 187241958166564053774, 5239429159586654676168
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170748, 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)/(378*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).
From G. C. Greubel, Apr 28 2019: (Start)
a(n) = 27*(a(n-1) + a(n-2) + a(n-3) -14*a(n-4)).
G.f.: (1+x)*(1-x^4)/(1 - 28*x + 405*x^4 - 378*x^5). (End)
MATHEMATICA
CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(378*t^4-27*t^3-27*t^2 - 27*t+1), {t, 0, 20}], t] (* or *) LinearRecurrence[{27, 27, 27, -378}, {1, 29, 812, 22736, 636202}, 20] (* G. C. Greubel, Dec 10 2016 *)
coxG[{4, 378, -27}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 28 2019 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^4)/(1-28*x+405*x^4-378*x^5)) \\ G. C. Greubel, Dec 10 2016, modified Apr 28 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-28*x+405*x^4-378*x^5) )); // G. C. Greubel, Apr 28 2019
(Sage) ((1+x)*(1-x^4)/(1-28*x+405*x^4-378*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019
(GAP) a:=[29, 812, 22736, 636202];; for n in [5..20] do a[n]:=27*(a[n-1] +a[n-2]+a[n-3] -14*a[n-4]); od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019
CROSSREFS
Sequence in context: A180844 A159669 A162831 * A163549 A164026 A164665
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved