A170580 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = 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, 41, 41, 41, -861).

Formula

G.f. (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)/(861*t^47 -

41*t^46 - 41*t^45 - 41*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)

Crossrefs

Sequence in context: A170436 A170484 A170532 * A170628 A170676 A170724

Adjacent sequences: A170577 A170578 A170579 * A170581 A170582 A170583

Keyword

nonn

Author

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

Status

approved