A170436 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.

1, 43, 1806, 75852, 3185784, 133802928, 5619722976, 236028364992, 9913191329664, 416354035845888, 17486869505527296, 734448519232146432, 30846837807750150144, 1295567187925506306048, 54413821892871264854016

Offset

0,2

Comments

The initial terms coincide with those of A170762, 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 (41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, -861).

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)/(861*t^44 - 41*t^43 - 41*t^42 - 41*t^41 -

41*t^40 - 41*t^39 - 41*t^38 - 41*t^37 - 41*t^36 - 41*t^35 - 41*t^34 -

41*t^33 - 41*t^32 - 41*t^31 - 41*t^30 - 41*t^29 - 41*t^28 - 41*t^27 -

41*t^26 - 41*t^25 - 41*t^24 - 41*t^23 - 41*t^22 - 41*t^21 - 41*t^20 -

41*t^19 - 41*t^18 - 41*t^17 - 41*t^16 - 41*t^15 - 41*t^14 - 41*t^13 -

41*t^12 - 41*t^11 - 41*t^10 - 41*t^9 - 41*t^8 - 41*t^7 - 41*t^6 - 41*t^5

- 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1)

Mathematica

coxG[{44, 861, -41}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 11 2017 *)

Crossrefs

Sequence in context: A170292 A170340 A170388 * A170484 A170532 A170580

Adjacent sequences: A170433 A170434 A170435 * A170437 A170438 A170439

Keyword

nonn

Author

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

Status

approved