A163214 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

1, 31, 930, 27900, 836535, 25082100, 752044965, 22548807900, 676088221260, 20271372436125, 607803134933490, 18223958540698875, 546414860017738110, 16383333982098029400, 491226816855341457015, 14728612983261055500600

Offset

0,2

Comments

The initial terms coincide with those of A170750, 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..670

Index entries for linear recurrences with constant coefficients, signature (29,29,29,-435).

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(435*t^4 - 29*t^3 - 29*t^2 - 29*t + 1).

a(n) = 29*(a(n-1) + a(n-2) + a(n-3) - 15*a(n-4)). - G. C. Greubel, Apr 28 2019

Mathematica

coxG[{4, 435, -29}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 24 2016 *)
CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(435*t^4-29*t^3-29*t^2 - 29*t+1), {t, 0, 20}], t] (* or *) LinearRecurrence[{29, 29, 29, -435}, {1, 31, 930, 27900, 836535}, 20] (* G. C. Greubel, Dec 10 2016 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^4)/(1-30*x+464*x^4-435*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)/(1-30*x+464*x^4-435*x^5) )); // G. C. Greubel, Apr 28 2019
(Sage) ((1+x)*(1-x^4)/(1-30*x+464*x^4-435*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019
(GAP) a:=[31, 930, 27900, 836535];; for n in [5..20] do a[n]:=29*(a[n-1]+ a[n-2] +a[n-3] -15*a[n-4]); od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019

Crossrefs

Sequence in context: A213467 A157878 A162835 * A163564 A164030 A164667

Adjacent sequences: A163211 A163212 A163213 * A163215 A163216 A163217

Keyword

nonn

Author

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

Status

approved