A170684 Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = 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.

About the initial comment, first disagreement is at index 50 and the difference is 3. - Vincenzo Librandi, Dec 09 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

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

Formula

G.f. (t^50 + 2*t^49 + 2*t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 +

2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*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^50 - t^49 - t^48 - t^47 - t^46 - t^45 - t^44 - t^43 - t^42 -

t^41 - t^40 - t^39 - 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

With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-t^Range[49]]+ t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 40}], t]] (* Vincenzo Librandi, Dec 09 2012 *)

Crossrefs

Sequence in context: A170540 A170588 A170636 * A003945 A007283 A049942

Adjacent sequences: A170681 A170682 A170683 * A170685 A170686 A170687

Keyword

nonn

Author

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

Status

approved