A163216 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

1, 33, 1056, 33792, 1080816, 34569216, 1105674768, 35364307968, 1131105025776, 36177678932736, 1157120181575952, 37009757234816256, 1183733679862288368, 37860973146888460800, 1210959282493490855952, 38731766829339020895744

Offset

0,2

Comments

The initial terms coincide with those of A170752, 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..660

Index entries for linear recurrences with constant coefficients, signature (31, 31, 31, -496).

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(496*t^4 - 31*t^3 - 31*t^2 - 31*t + 1).

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

a(n) = 31*(a(n-1) + a(n-2) + a(n-3) - 16*a(n-4)).

G.f.: (1+x)*(1-x^4)/(1 - 32*x + 527*x^4 - 496*x^5). (End)

Mathematica

CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(496*t^4-31*t^3-31*t^2 - 31*t+1), {t, 0, 20}], t] (* or *) LinearRecurrence[{31, 31, 31, -496}, {1, 33, 1056, 33792, 1080816}, 20] (* G. C. Greubel, Dec 11 2016 *)
coxG[{4, 496, -31}] (* 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)/(1-32*x+527*x^4-496*x^5)) \\ G. C. Greubel, Dec 11 2016, modified Apr 28 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-32*x+527*x^4-496*x^5) )); // G. C. Greubel, Apr 28 2019
(Sage) ((1+x)*(1-x^4)/(1-32*x+527*x^4-496*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019
(GAP) a:=[33, 1056, 33792, 1080816];; for n in [5..20] do a[n]:=31*(a[n-1]+ a[n-2]+a[n-3]-16*a[n-4]); od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019

Crossrefs

Sequence in context: A159675 A162837 A324951 * A163567 A164049 A164669

Adjacent sequences: A163213 A163214 A163215 * A163217 A163218 A163219

Keyword

nonn

Author

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

Status

approved