A170407 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = 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, 12, -78).

Formula

G.f. (t^44 + 2*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^44 - 12*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[{44, 78, -12}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Feb 23 2017 *)

Crossrefs

Sequence in context: A170263 A170311 A170359 * A170455 A170503 A170551

Adjacent sequences: A170404 A170405 A170406 * A170408 A170409 A170410

Keyword

nonn

Author

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

Status

approved