A170428 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.

1, 35, 1190, 40460, 1375640, 46771760, 1590239840, 54068154560, 1838317255040, 62502786671360, 2125094746826240, 72253221392092160, 2456609527331133440, 83524723929258536960, 2839840613594790256640, 96554580862222868725760

Offset

0,2

Comments

The initial terms coincide with those of A170754, 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..15.

Index entries for linear recurrences with constant coefficients, signature (33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, -561).

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)/(561*t^44 - 33*t^43 - 33*t^42 - 33*t^41 -

33*t^40 - 33*t^39 - 33*t^38 - 33*t^37 - 33*t^36 - 33*t^35 - 33*t^34 -

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

33*t^26 - 33*t^25 - 33*t^24 - 33*t^23 - 33*t^22 - 33*t^21 - 33*t^20 -

33*t^19 - 33*t^18 - 33*t^17 - 33*t^16 - 33*t^15 - 33*t^14 - 33*t^13 -

33*t^12 - 33*t^11 - 33*t^10 - 33*t^9 - 33*t^8 - 33*t^7 - 33*t^6 - 33*t^5

- 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1)

Mathematica

coxG[{44, 561, -33}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Feb 19 2023 *)

Crossrefs

Sequence in context: A170284 A170332 A170380 * A170476 A170524 A170572

Adjacent sequences: A170425 A170426 A170427 * A170429 A170430 A170431

Keyword

nonn

Author

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

Status

approved