A164742 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

1, 7, 42, 252, 1512, 9072, 54432, 326592, 1959531, 11757060, 70541625, 423245340, 2539445580, 15236514720, 91418135760, 548503099200, 3290984303460, 19745700072525, 118472965958550, 710830388968875, 4264937893581750

Offset

0,2

Comments

The initial terms coincide with those of A003949, 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..20.

Index entries for linear recurrences with constant coefficients, signature (5, 5, 5, 5, 5, 5, 5, -15).

Formula

G.f.: (t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(15*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1).

Mathematica

coxG[{8, 15, -5}] (* The coxG program is at A169452 *)  (* Harvey P. Dale, Dec 19 2024 *)

Crossrefs

Sequence in context: A163345 A163923 A164369 * A165214 A165782 A166365

Adjacent sequences: A164739 A164740 A164741 * A164743 A164744 A164745

Keyword

nonn

Author

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

Status

approved