A170437 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = 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, -903).

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)/(903*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[{44, 903, -42}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 09 2017 *)

Crossrefs

Sequence in context: A170293 A170341 A170389 * A170485 A170533 A170581

Adjacent sequences: A170434 A170435 A170436 * A170438 A170439 A170440

Keyword

nonn

Author

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

Status

approved