A169112 Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = 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, 100663293, 201326580, 402653151, 805306284, 1610612532, 3221224992

Offset

0,2

Comments

The initial terms coincide with those of A003945, although the two sequences are eventually different.

First disagreement at index 26: a(26) = 100663293, A003945(26) = 100663296. - Klaus Brockhaus, Apr 30 2011

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).

Formula

G.f.: (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^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).

Crossrefs

Cf. A003945 (G.f.: (1+x)/(1-2*x)).

Sequence in context: A168968 A169016 A169064 * A169160 A169208 A169256

Adjacent sequences: A169109 A169110 A169111 * A169113 A169114 A169115

Keyword

nonn

Author

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

Status

approved