A169551 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204890, 34867844010, 313810596090, 2824295364810, 25418658283290, 228767924549610, 2058911320946490, 18530201888518410, 166771816996665690

Offset

0,2

Comments

The initial terms coincide with those of A003952, 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..18.

Index entries for linear recurrences with constant coefficients, signature (8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -36).

Formula

G.f. (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)/(36*t^35 - 8*t^34 - 8*t^33 - 8*t^32 - 8*t^31 - 8*t^30

- 8*t^29 - 8*t^28 - 8*t^27 - 8*t^26 - 8*t^25 - 8*t^24 - 8*t^23 - 8*t^22

- 8*t^21 - 8*t^20 - 8*t^19 - 8*t^18 - 8*t^17 - 8*t^16 - 8*t^15 - 8*t^14

- 8*t^13 - 8*t^12 - 8*t^11 - 8*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 -

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

Crossrefs

Sequence in context: A169407 A169455 A169503 * A170019 A170067 A170115

Adjacent sequences: A169548 A169549 A169550 * A169552 A169553 A169554

Keyword

nonn

Author

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

Status

approved