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

Author

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

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A154638, A170753.

Programs

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

Magma

R:=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

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 *)

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

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

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). (End)