A170598 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.

1, 13, 156, 1872, 22464, 269568, 3234816, 38817792, 465813504, 5589762048, 67077144576, 804925734912, 9659108818944, 115909305827328, 1390911669927936, 16690940039135232, 200291280469622784

Offset

0,2

Comments

The initial terms coincide with those of A170732, 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..16.

Index entries for linear recurrences with constant coefficients, signature (11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, -66).

Formula

G.f. (t^48 + 2*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)/(66*t^48 - 11*t^47 - 11*t^46 - 11*t^45 - 11*t^44 - 11*t^43 - 11*t^42

- 11*t^41 - 11*t^40 - 11*t^39 - 11*t^38 - 11*t^37 - 11*t^36 - 11*t^35 -

11*t^34 - 11*t^33 - 11*t^32 - 11*t^31 - 11*t^30 - 11*t^29 - 11*t^28 -

11*t^27 - 11*t^26 - 11*t^25 - 11*t^24 - 11*t^23 - 11*t^22 - 11*t^21 -

11*t^20 - 11*t^19 - 11*t^18 - 11*t^17 - 11*t^16 - 11*t^15 - 11*t^14 -

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

11*t^6 - 11*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1)

Crossrefs

Sequence in context: A170454 A170502 A170550 * A170646 A170694 A170732

Adjacent sequences: A170595 A170596 A170597 * A170599 A170600 A170601

Keyword

nonn

Author

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

Status

approved