A170492 Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = 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, 1, 1, 1, 1, 1, 1, 1, -1).

Formula

G.f. (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^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[2t^Range[45]]+t^46+1, den=Total[-t^Range[45]]+t^46+1}, CoefficientList[ Series[ num/den, {t, 0, 40}], t]] (* Harvey P. Dale, Jan 16 2012 *)
coxG[{46, 46, -1, 40}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 23 2025 *)

Crossrefs

Sequence in context: A170348 A170396 A170444 * A170540 A170588 A170636

Adjacent sequences: A170489 A170490 A170491 * A170493 A170494 A170495

Keyword

nonn

Author

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

Status

approved