A170191 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.

1, 38, 1406, 52022, 1924814, 71218118, 2635070366, 97497603542, 3607411331054, 133474219248998, 4938546112212926, 182726206151878262, 6760869627619495694, 250152176221921340678, 9255630520211089605086

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

Table of n, a(n) for n=0..14.

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

Formula

G.f. (t^39 + 2*t^38 + 2*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)/(666*t^39 -

36*t^38 - 36*t^37 - 36*t^36 - 36*t^35 - 36*t^34 - 36*t^33 - 36*t^32 -

36*t^31 - 36*t^30 - 36*t^29 - 36*t^28 - 36*t^27 - 36*t^26 - 36*t^25 -

36*t^24 - 36*t^23 - 36*t^22 - 36*t^21 - 36*t^20 - 36*t^19 - 36*t^18 -

36*t^17 - 36*t^16 - 36*t^15 - 36*t^14 - 36*t^13 - 36*t^12 - 36*t^11 -

36*t^10 - 36*t^9 - 36*t^8 - 36*t^7 - 36*t^6 - 36*t^5 - 36*t^4 - 36*t^3 -

36*t^2 - 36*t + 1)

Mathematica

coxG[{39, 666, -36}] (* The coxG program is at A169452 *)  (* Harvey P. Dale, Jul 20 2024 *)

Crossrefs

Sequence in context: A170047 A170095 A170143 * A170239 A170287 A170335

Adjacent sequences: A170188 A170189 A170190 * A170192 A170193 A170194

Keyword

nonn

Author

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

Status

approved