A170588 - OEIS

A170588

Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = 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

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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, 1, -1).

FORMULA

G.f. (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^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[2t^Range[47]]+t^48+1, den=Total[-t^Range[47]]+t^48+ 1}, CoefficientList[Series[num/den, {t, 0, 40}], t]] (* Harvey P. Dale, Jun 19 2014 *)

CROSSREFS

Sequence in context: A170444 A170492 A170540 * A170636 A170684 A003945

Adjacent sequences: A170585 A170586 A170587 * A170589 A170590 A170591

KEYWORD

nonn

AUTHOR

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

STATUS

approved