A163110 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

1, 19, 342, 6156, 110637, 1988388, 35735751, 642249324, 11542621410, 207446086881, 3728258709552, 67004941956759, 1204224973728534, 21642549713419572, 388963830112221249, 6990528525469894908, 125635046969043641691, 2257935858412484688900, 40580032910411799982386

Offset

0,2

Comments

The initial terms coincide with those of A170738, 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 (17,17,17,-153).

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(153*t^4 - 17*t^3 - 17*t^2 - 17*t + 1).

Mathematica

coxG[{4, 153, -17}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 24 2019 *)

Prog

(PARI) Vec((t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(153*t^4 - 17*t^3 - 17*t^2 - 17*t + 1) + O(t^20)) \\ Jinyuan Wang, Mar 23 2020

Crossrefs

Sequence in context: A049629 A162805 A049664 * A163453 A163968 A164631

Adjacent sequences: A163107 A163108 A163109 * A163111 A163112 A163113

Keyword

nonn

Author

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

Extensions

More terms from Jinyuan Wang, Mar 23 2020

Status

approved