A163092 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

1, 16, 240, 3600, 53880, 806400, 12069120, 180633600, 2703470280, 40461750000, 605574696720, 9063392310000, 135648138214680, 2030190989349600, 30385049935084320, 454760790684530400, 6806221388012959080, 101865971146974325200, 1524586916316221551920

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..18.

Index entries for linear recurrences with constant coefficients, signature (14,14,14,-105).

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(105*t^4 - 14*t^3 - 14*t^2 - 14*t + 1).

Mathematica

CoefficientList[ Series[(t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(105*t^4 - 14*t^3 - 14*t^2 - 14*t + 1), {t, 0, 16}], t] (* Jean-François Alcover, Nov 26 2013 *)

Prog

(PARI) Vec((t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(105*t^4 - 14*t^3 - 14*t^2 - 14*t + 1) + O(t^20)) \\ Jinyuan Wang, Mar 23 2020

Crossrefs

Sequence in context: A097829 A010559 A342884 * A163441 A163964 A164627

Adjacent sequences: A163089 A163090 A163091 * A163093 A163094 A163095

Keyword

nonn

Author

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

Extensions

More terms from Jinyuan Wang, Mar 23 2020

Status

approved