A169489 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = 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, -903).

Formula

G.f. (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^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[{33, 903, -42}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 15 2017 *)

Crossrefs

Sequence in context: A169345 A169393 A169441 * A169537 A170005 A170053

Adjacent sequences: A169486 A169487 A169488 * A169490 A169491 A169492

Keyword

nonn

Author

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

Status

approved