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A162987 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I. 2
1, 11, 110, 1100, 10945, 108900, 1083555, 10781100, 107269470, 1067306625, 10619454780, 105661128375, 1051303881870, 10460231387100, 104076892111005, 1035541095642900, 10303395297584895, 102516409155629700 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A003953, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..995

Index entries for linear recurrences with constant coefficients, signature (9, 9, 9, -45).

FORMULA

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(45*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).

From G. C. Greubel, Apr 28 2019: (Start)

a(n) = 9*(a(n-1) + a(n-2) + a(n-3) - 5*a(n-4)).

G.f.: ((1+x)*(1-x^4)/(1 - 10*x + 54*x^4 - 45*x^5). (End)

MATHEMATICA

CoefficientList[Series[(1+x)*(1-x^4)/(1-10*x+54*x^4-45*x^5), {x, 0, 20}], x] (* or *) coxG[{4, 45, -9}] (* 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)/(1-10*x+54*x^4-45*x^5)) \\ G. C. Greubel, Apr 28 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-10*x+54*x^4-45*x^5) )); // G. C. Greubel, Apr 28 2019

(Sage) ((1+x)*(1-x^4)/(1-10*x+54*x^4-45*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019

(GAP) a:=[11, 110, 1100, 10945];; for n in [5..20] do a[n]:=9*(a[n-1]+a[n-2] +a[n-3] -5*a[n-4]); od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019

CROSSREFS

Sequence in context: A097784 A121031 A115804 * A163404 A115808 A163955

Adjacent sequences:  A162984 A162985 A162986 * A162988 A162989 A162990

KEYWORD

nonn

AUTHOR

John Cannon and N. J. A. Sloane, Dec 03 2009

STATUS

approved

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Last modified August 24 03:51 EDT 2019. Contains 326260 sequences. (Running on oeis4.)