A168955 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.

1, 38, 1406, 52022, 1924814, 71218118, 2635070366, 97497603542, 3607411331054, 133474219248998, 4938546112212926, 182726206151878262, 6760869627619495694, 250152176221921340678, 9255630520211089605086

Offset

0,2

Comments

The initial terms coincide with those of A170757, although the two sequences are eventually different.

First disagreement at index 22: a(22) = 32510212035325589169720872824241503, A170757(22) = 32510212035325589169720872824242206. - Klaus Brockhaus, Apr 10 2011

Computed with MAGMA using commands similar to those used to compute A154638.

Links

Table of n, a(n) for n=0..14.

Index entries for linear recurrences with constant coefficients, signature (36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, -666).

Formula

G.f.: (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)/(666*t^22 - 36*t^21 - 36*t^20 - 36*t^19 - 36*t^18 - 36*t^17 - 36*t^16 - 36*t^15 - 36*t^14 - 36*t^13 - 36*t^12 - 36*t^11 - 36*t^10 - 36*t^9 - 36*t^8 - 36*t^7 - 36*t^6 - 36*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1).

Mathematica

coxG[{22, 666, -36}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 08 2019 *)

Crossrefs

Cf. A170757 (G.f.: (1+x)/(1-37*x)).

Sequence in context: A168811 A168859 A168907 * A169003 A169051 A169099

Adjacent sequences: A168952 A168953 A168954 * A168956 A168957 A168958

Keyword

nonn

Author

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

Status

approved