A170518 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.

1, 29, 812, 22736, 636608, 17825024, 499100672, 13974818816, 391294926848, 10956257951744, 306775222648832, 8589706234167296, 240511774556684288, 6734329687587160064, 188561231252440481792, 5279714475068333490176

Offset

0,2

Comments

The initial terms coincide with those of A170748, 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 (27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, -378).

Formula

G.f. (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)/(378*t^46 - 27*t^45 -

27*t^44 - 27*t^43 - 27*t^42 - 27*t^41 - 27*t^40 - 27*t^39 - 27*t^38 -

27*t^37 - 27*t^36 - 27*t^35 - 27*t^34 - 27*t^33 - 27*t^32 - 27*t^31 -

27*t^30 - 27*t^29 - 27*t^28 - 27*t^27 - 27*t^26 - 27*t^25 - 27*t^24 -

27*t^23 - 27*t^22 - 27*t^21 - 27*t^20 - 27*t^19 - 27*t^18 - 27*t^17 -

27*t^16 - 27*t^15 - 27*t^14 - 27*t^13 - 27*t^12 - 27*t^11 - 27*t^10 -

27*t^9 - 27*t^8 - 27*t^7 - 27*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 -

27*t + 1)

Crossrefs

Sequence in context: A170374 A170422 A170470 * A170566 A170614 A170662

Adjacent sequences: A170515 A170516 A170517 * A170519 A170520 A170521

Keyword

nonn

Author

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

Status

approved