A170359 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

1, 14, 182, 2366, 30758, 399854, 5198102, 67575326, 878479238, 11420230094, 148462991222, 1930018885886, 25090245516518, 326173191714734, 4240251492291542, 55123269399790046, 716602502197270598

Offset

0,2

Comments

The initial terms coincide with those of A170733, 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..16.

Index entries for linear recurrences with constant coefficients, signature (12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, -78).

Formula

G.f. (t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*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)/(78*t^43 - 12*t^42 - 12*t^41 - 12*t^40 - 12*t^39 -

12*t^38 - 12*t^37 - 12*t^36 - 12*t^35 - 12*t^34 - 12*t^33 - 12*t^32 -

12*t^31 - 12*t^30 - 12*t^29 - 12*t^28 - 12*t^27 - 12*t^26 - 12*t^25 -

12*t^24 - 12*t^23 - 12*t^22 - 12*t^21 - 12*t^20 - 12*t^19 - 12*t^18 -

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

12*t^10 - 12*t^9 - 12*t^8 - 12*t^7 - 12*t^6 - 12*t^5 - 12*t^4 - 12*t^3 -

12*t^2 - 12*t + 1)

Mathematica

coxG[{43, 78, -12}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 16 2017 *)

Crossrefs

Sequence in context: A170215 A170263 A170311 * A170407 A170455 A170503

Adjacent sequences: A170356 A170357 A170358 * A170360 A170361 A170362

Keyword

nonn

Author

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

Status

approved