A170596 - OEIS

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A170596

Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.

1, 11, 110, 1100, 11000, 110000, 1100000, 11000000, 110000000, 1100000000, 11000000000, 110000000000, 1100000000000, 11000000000000, 110000000000000, 1100000000000000, 11000000000000000, 110000000000000000

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OFFSET

0,2

COMMENTS

The initial terms coincide with those of A003953, 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..17.

Index entries for linear recurrences with constant coefficients, signature (9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, -45).

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)/(45*t^48 - 9*t^47 - 9*t^46 - 9*t^45 - 9*t^44 - 9*t^43 - 9*t^42 -

9*t^41 - 9*t^40 - 9*t^39 - 9*t^38 - 9*t^37 - 9*t^36 - 9*t^35 - 9*t^34 -

9*t^33 - 9*t^32 - 9*t^31 - 9*t^30 - 9*t^29 - 9*t^28 - 9*t^27 - 9*t^26 -

9*t^25 - 9*t^24 - 9*t^23 - 9*t^22 - 9*t^21 - 9*t^20 - 9*t^19 - 9*t^18 -

9*t^17 - 9*t^16 - 9*t^15 - 9*t^14 - 9*t^13 - 9*t^12 - 9*t^11 - 9*t^10 -

9*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1)

MATHEMATICA

coxG[{48, 45, -9}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 14 2020 *)

CROSSREFS

Sequence in context: A170452 A170500 A170548 * A170644 A170692 A278664

Adjacent sequences: A170593 A170594 A170595 * A170597 A170598 A170599

KEYWORD

nonn

AUTHOR

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

STATUS

approved