A170389 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

1, 44, 1892, 81356, 3498308, 150427244, 6468371492, 278139974156, 11960018888708, 514280812214444, 22114074925221092, 950905221784506956, 40888924536733799108, 1758223755079553361644, 75603621468420794550692

Offset

0,2

Comments

The initial terms coincide with those of A170763, 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 (42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, -903).

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)/(903*t^43 - 42*t^42 - 42*t^41 - 42*t^40 - 42*t^39 -

42*t^38 - 42*t^37 - 42*t^36 - 42*t^35 - 42*t^34 - 42*t^33 - 42*t^32 -

42*t^31 - 42*t^30 - 42*t^29 - 42*t^28 - 42*t^27 - 42*t^26 - 42*t^25 -

42*t^24 - 42*t^23 - 42*t^22 - 42*t^21 - 42*t^20 - 42*t^19 - 42*t^18 -

42*t^17 - 42*t^16 - 42*t^15 - 42*t^14 - 42*t^13 - 42*t^12 - 42*t^11 -

42*t^10 - 42*t^9 - 42*t^8 - 42*t^7 - 42*t^6 - 42*t^5 - 42*t^4 - 42*t^3 -

42*t^2 - 42*t + 1)

Mathematica

coxG[{43, 903, -42}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 01 2019 *)

Crossrefs

Sequence in context: A170245 A170293 A170341 * A170437 A170485 A170533

Adjacent sequences: A170386 A170387 A170388 * A170390 A170391 A170392

Keyword

nonn

Author

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

Status

approved