A170601 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.

1, 16, 240, 3600, 54000, 810000, 12150000, 182250000, 2733750000, 41006250000, 615093750000, 9226406250000, 138396093750000, 2075941406250000, 31139121093750000, 467086816406250000, 7006302246093750000

Offset

0,2

Comments

The initial terms coincide with those of A170735, 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 (14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, -105).

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)/(105*t^48 - 14*t^47 - 14*t^46 - 14*t^45 - 14*t^44 - 14*t^43 - 14*t^42

- 14*t^41 - 14*t^40 - 14*t^39 - 14*t^38 - 14*t^37 - 14*t^36 - 14*t^35 -

14*t^34 - 14*t^33 - 14*t^32 - 14*t^31 - 14*t^30 - 14*t^29 - 14*t^28 -

14*t^27 - 14*t^26 - 14*t^25 - 14*t^24 - 14*t^23 - 14*t^22 - 14*t^21 -

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

14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 -

14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1)

Mathematica

coxG[{48, 105, -14}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 06 2016 *)

Crossrefs

Sequence in context: A170457 A170505 A170553 * A170649 A170697 A170735

Adjacent sequences: A170598 A170599 A170600 * A170602 A170603 A170604

Keyword

nonn

Author

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

Status

approved