A163217 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

1, 34, 1122, 37026, 1221297, 40284288, 1328771136, 43829305344, 1445702699760, 47686274735616, 1572924224543232, 51882656590093824, 1711341215834452224, 56448319139710451712, 1861938872397761101824, 61415759005426222645248

Offset

0,2

Comments

The initial terms coincide with those of A170753, 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..650

Index entries for linear recurrences with constant coefficients, signature (32, 32, 32, -528).

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(528*t^4 - 32*t^3 - 32*t^2 - 32*t + 1).

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

a(n) = 32*(a(n-1) + a(n-2) + a(n-3)) - 528*a(n-4).

G.f.: (1+x)*(1-x^4)/(1 - 33*x + 560*x^4 - 528*x^5).

Mathematica

CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(528*t^4-32*t^3-32*t^2 - 32*t+1), {t, 0, 20}], t] (* or *)
LinearRecurrence[{32, 32, 32, -528}, {1, 34, 1122, 37026, 1221297}, 20] (* G. C. Greubel, Dec 11 2016; simplified by Georg Fischer, Apr 08 2019 *)
coxG[{4, 528, -32}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 06 2018 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^4)/(1-33*x+560*x^4-528*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)/(1-33*x+560*x^4-528*x^5) )); // G. C. Greubel, Apr 28 2019
(Sage) ((1+x)*(1-x^4)/(1-33*x+560*x^4-528*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019
(GAP) a:=[34, 1122, 37026, 1221297];; for n in [5..20] do a[n]:=32*(a[n-1]+ a[n-2]+a[n-3]) -528*a[n-4]; od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019

Crossrefs

Cf. A154638, A170753.

Sequence in context: A214190 A214241 A162838 * A163593 A164050 A164670

Adjacent sequences: A163214 A163215 A163216 * A163218 A163219 A163220

Keyword

nonn,easy

Author

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

Status

approved