A164668 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117296, 880403620800, 27292511768640, 846067850066880, 26228102894483520, 813071175543706560, 25205206002111144000, 781361372433389169360, 24222202122841326496800

Offset

0,2

Comments

The initial terms coincide with those of A170751, 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..15.

Index entries for linear recurrences with constant coefficients, signature (30, 30, 30, 30, 30, 30, -465).

Formula

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(465*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).

Mathematica

coxG[{7, 465, -30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 06 2025 *)

Crossrefs

Sequence in context: A163215 A163565 A164036 * A165131 A165548 A166128

Adjacent sequences: A164665 A164666 A164667 * A164669 A164670 A164671

Keyword

nonn

Author

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

Status

approved