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A170636 Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I. 0
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 (list; graph; refs; listen; history; text; internal format)
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.

FORMULA

G.f. (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)/(t^48 - 2*t^47 + 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

Sequence in context: A170540 A170588 * A170684 A003945 A007283 A049942

Adjacent sequences:  A170633 A170634 A170635 * A170637 A170638 A170639

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified November 27 02:34 EST 2014. Contains 250152 sequences.