A170108 Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.

1, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608, 393216, 786432, 1572864, 3145728, 6291456, 12582912, 25165824, 50331648, 100663296, 201326592, 402653184, 805306368, 1610612736, 3221225472

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 (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1).

Formula

G.f. (t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 +

2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 +

2*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)/(t^38 - t^37 - t^36 -

t^35 - t^34 - t^33 - t^32 - t^31 - t^30 - t^29 - t^28 - t^27 - t^26 -

t^25 - t^24 - t^23 - t^22 - t^21 - t^20 - t^19 - t^18 - t^17 - t^16 -

t^15 - t^14 - t^13 - t^12 - t^11 - t^10 - t^9 - t^8 - t^7 - t^6 - t^5 -

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

Mathematica

coxG[{38, 1, -1, 40}] (* coxG program from A169452 *) (* Harvey P. Dale, Aug 25 2014 *)

Crossrefs

Sequence in context: A169544 A170012 A170060 * A170156 A170204 A170252

Adjacent sequences: A170105 A170106 A170107 * A170109 A170110 A170111

Keyword

nonn

Author

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

Status

approved