A170310 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

1, 13, 156, 1872, 22464, 269568, 3234816, 38817792, 465813504, 5589762048, 67077144576, 804925734912, 9659108818944, 115909305827328, 1390911669927936, 16690940039135232, 200291280469622784

Offset

0,2

Comments

The initial terms coincide with those of A170732, 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 (11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, -66).

Formula

G.f. (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)/(66*t^42 - 11*t^41 - 11*t^40 - 11*t^39 - 11*t^38 - 11*t^37 -

11*t^36 - 11*t^35 - 11*t^34 - 11*t^33 - 11*t^32 - 11*t^31 - 11*t^30 -

11*t^29 - 11*t^28 - 11*t^27 - 11*t^26 - 11*t^25 - 11*t^24 - 11*t^23 -

11*t^22 - 11*t^21 - 11*t^20 - 11*t^19 - 11*t^18 - 11*t^17 - 11*t^16 -

11*t^15 - 11*t^14 - 11*t^13 - 11*t^12 - 11*t^11 - 11*t^10 - 11*t^9 -

11*t^8 - 11*t^7 - 11*t^6 - 11*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1)

Mathematica

coxG[{42, 66, -11}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 14 2023 *)

Crossrefs

Sequence in context: A170166 A170214 A170262 * A170358 A170406 A170454

Adjacent sequences: A170307 A170308 A170309 * A170311 A170312 A170313

Keyword

nonn

Author

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

Status

approved