A169546 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

1, 5, 20, 80, 320, 1280, 5120, 20480, 81920, 327680, 1310720, 5242880, 20971520, 83886080, 335544320, 1342177280, 5368709120, 21474836480, 85899345920, 343597383680, 1374389534720, 5497558138880, 21990232555520, 87960930222080

Offset

0,2

Comments

The initial terms coincide with those of A003947, 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..1000

Index entries for linear recurrences with constant coefficients, signature (3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -6).

Formula

G.f.: (t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(6*t^35 - 3*t^34 - 3*t^33 - 3*t^32 - 3*t^31 - 3*t^30 - 3*t^29 - 3*t^28 - 3*t^27 - 3*t^26 - 3*t^25 - 3*t^24 - 3*t^23 - 3*t^22 - 3*t^21 - 3*t^20 - 3*t^19 - 3*t^18 - 3*t^17 - 3*t^16 - 3*t^15 - 3*t^14 - 3*t^13 - 3*t^12 - 3*t^11 - 3*t^10 - 3*t^9 - 3*t^8 - 3*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1).

G.f.: (1+x)*(1-x^35)/(1 - 4*x + 9*x^35 - 6*x^36). - G. C. Greubel, Apr 25 2019

Mathematica

coxG[{35, 6, -3, 30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 16 2015 *)
CoefficientList[Series[(1+x)*(1-x^35)/(1-4*x+9*x^35-6*x^36), {x, 0, 25}], x] (* G. C. Greubel, Apr 25 2019 *)

Prog

(PARI) my(x='x+O('x^25)); Vec((1+x)*(1-x^35)/(1-4*x+9*x^35-6*x^36)) \\ G. C. Greubel, Apr 25 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 25); Coefficients(R!( (1+x)*(1-x^35)/(1-4*x+9*x^35-6*x^36) )); // G. C. Greubel, Apr 25 2019
(Sage) ((1+x)*(1-x^35)/(1-4*x+9*x^35-6*x^36)).series(x, 25).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019

Crossrefs

Sequence in context: A169402 A169450 A169498 * A170014 A170062 A170110

Adjacent sequences: A169543 A169544 A169545 * A169547 A169548 A169549

Keyword

nonn

Author

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

Status

approved