A163660 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 38, 1406, 52022, 1924814, 71217415, 2635018344, 97494717024, 3607268946840, 133467634460304, 4938253762332042, 182713586854206456, 6760336027236505128, 250129965636431546040, 9254717436709694665512

Offset

0,2

Comments

The initial terms coincide with those of A170757, 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..635

Index entries for linear recurrences with constant coefficients, signature (36, 36, 36, 36, -666).

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(666*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1).

a(n) = 36*a(n-1)+36*a(n-2)+36*a(n-3)+36*a(n-4)-666*a(n-5). - Wesley Ivan Hurt, May 11 2021

Mathematica

CoefficientList[Series[(1+x)*(1-x^5)/(1-37*x+702*x^5-666*x^6), {x, 0, 20}], x] (* G. C. Greubel, Aug 01 2017 *)
coxG[{5, 666, -36}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 22 2019 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-37*x+702*x^5-666*x^6)) \\ G. C. Greubel, Aug 01 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-37*x+702*x^5-666*x^6) )); // G. C. Greubel, Apr 28 2019
(Sage) ((1+x)*(1-x^5)/(1-37*x+702*x^5-666*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019
(GAP) a:=[38, 1406, 52022, 1924814, 71217415];; for n in [6..20] do a[n]:=36*(a[n-1]+a[n-2] +a[n-3]+a[n-4]) - 666*a[n-5]; od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019

Crossrefs

Sequence in context: A268885 A162858 A163221 * A164071 A164674 A165170

Adjacent sequences: A163657 A163658 A163659 * A163661 A163662 A163663

Keyword

nonn

Author

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

Status

approved