A170156 Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = 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 (2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1).

Formula

G.f. (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)/(t^38 - 2*t^37 + t^36 - 2*t^35 +

t^34 - 2*t^33 + t^32 - 2*t^31 + t^30 - 2*t^29 + t^28 - 2*t^27 + t^26 -

2*t^25 + t^24 - 2*t^23 + t^22 - 2*t^21 + t^20 - 2*t^19 + t^18 - 2*t^17 +

t^16 - 2*t^15 + t^14 - 2*t^13 + t^12 - 2*t^11 + t^10 - 2*t^9 + t^8 -

2*t^7 + t^6 - 2*t^5 + t^4 - 2*t^3 + t^2 - 2*t + 1)

Crossrefs

Sequence in context: A170012 A170060 A170108 * A170204 A170252 A170300

Adjacent sequences: A170153 A170154 A170155 * A170157 A170158 A170159

Keyword

nonn

Author

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

Status

approved