A165183 Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 3, 6, 12, 24, 48, 96, 192, 384, 765, 1524, 3039, 6060, 12084, 24096, 48048, 95808, 191040, 380934, 759585, 1514616, 3020151, 6022194, 12008280, 23944560, 47745552, 95204832, 189838836, 378539436, 754809225, 1505092764, 3001161291

Offset

0,2

Comments

The initial terms coincide with those of A003945, 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..31.

Index entries for linear recurrences with constant coefficients, signature (2, -1, 2, -1, 2, -1, 2, -1).

Formula

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

+ t^4 - 2*t^3 + t^2 - 2*t + 1)

Mathematica

LinearRecurrence[{2, -1, 2, -1, 2, -1, 2, -1}, {1, 3, 6, 12, 24, 48, 96, 192, 384}, 40] (* Harvey P. Dale, Aug 14 2024 *)

Crossrefs

Sequence in context: A356040 A164696 A344040 * A046944 A165745 A166327

Adjacent sequences: A165180 A165181 A165182 * A165184 A165185 A165186

Keyword

nonn

Author

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

Status

approved