A170629 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = 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, 42, 42, 42, 42, 42, -903).

Formula

G.f. (t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*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)/(903*t^48 - 42*t^47 - 42*t^46 - 42*t^45 - 42*t^44 - 42*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[{48, 903, -42}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 27 2019 *)

Crossrefs

Sequence in context: A170485 A170533 A170581 * A170677 A170725 A063821

Adjacent sequences: A170626 A170627 A170628 * A170630 A170631 A170632

Keyword

nonn

Author

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

Status

approved