A170540 - OEIS

A170540

Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = 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 (2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1).

FORMULA

G.f. (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)/(t^46 - 2*t^45 + t^44 - 2*t^43 + t^42 - 2*t^41

+ t^40 - 2*t^39 + t^38 - 2*t^37 + t^36 - 2*t^35 + t^34 - 2*t^33 + t^32 -

2*t^31 + t^30 - 2*t^29 + t^28 - 2*t^27 + t^26 - 2*t^25 + t^24 - 2*t^23 +

t^22 - 2*t^21 + t^20 - 2*t^19 + 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)

CROSSREFS