A168776 Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

1, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608, 393216, 786429, 1572852, 3145695, 6291372, 12582708, 25165344, 50330544, 100660800, 201321024, 402640896, 805279488, 1610554368, 3221099520

Offset

0,2

Comments

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

First disagreement at index 19: a(19) = 786429, A003945(19) = 786432.

Computed with MAGMA using commands similar to those used to compute A154638.

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

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).

Formula

G.f.: (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^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).

Mathematica

CoefficientList[Series[(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^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), {t, 0, 50}], t] (* G. C. Greubel, Aug 12 2016 *)

Crossrefs

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

Sequence in context: A167881 A168680 A168728 * A168824 A168872 A168920

Adjacent sequences: A168773 A168774 A168775 * A168777 A168778 A168779

Keyword

nonn,easy

Author

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

Status

approved