A170086 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.

1, 29, 812, 22736, 636608, 17825024, 499100672, 13974818816, 391294926848, 10956257951744, 306775222648832, 8589706234167296, 240511774556684288, 6734329687587160064, 188561231252440481792, 5279714475068333490176, 147832005301913337724928, 4139296148453573456297984

Offset

0,2

Comments

The initial terms coincide with those of A170748, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

Links

Table of n, a(n) for n=0..17.

Index entries for linear recurrences with constant coefficients, signature (27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, -378).

Formula

G.f. (t^37 + 2*t^36 + 2*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)/(378*t^37 - 27*t^36 - 27*t^35 -

27*t^34 - 27*t^33 - 27*t^32 - 27*t^31 - 27*t^30 - 27*t^29 - 27*t^28 -

27*t^27 - 27*t^26 - 27*t^25 - 27*t^24 - 27*t^23 - 27*t^22 - 27*t^21 -

27*t^20 - 27*t^19 - 27*t^18 - 27*t^17 - 27*t^16 - 27*t^15 - 27*t^14 -

27*t^13 - 27*t^12 - 27*t^11 - 27*t^10 - 27*t^9 - 27*t^8 - 27*t^7 -

27*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1)

Mathematica

With[{num=Total[2t^Range[36]]+t^37+1, den=Total[-27 t^Range[36]]+ 378t^37+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Mar 28 2012 *)

Crossrefs

Cf. A154638, A170748.

Sequence in context: A170662 A170710 A170748 * A218731 A171334 A097782

Adjacent sequences: A170083 A170084 A170085 * A170087 A170088 A170089

Keyword

nonn

Author

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

Status

approved