A166855 - OEIS

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A166855

Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

1, 49, 2352, 112896, 5419008, 260112384, 12485394432, 599298932736, 28766348771328, 1380784741023744, 66277667569139712, 3181328043318706176, 152703746079297895272, 7329779811806298916608, 351829430966702345288856

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OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170768, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, -1128).

FORMULA

G.f.: (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)/(1128*t^12 - 47*t^11 - 47*t^10 - 47*t^9 -47*t^8 -47*t^7 -47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).

MATHEMATICA

CoefficientList[Series[(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)/(1128*t^12 - 47*t^11 - 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1), {t, 0, 50}], t] (* G. C. Greubel, May 25 2016 *)

CROSSREFS

Sequence in context: A165709 A166324 A166443 * A167102 A167646 A167879

Adjacent sequences: A166852 A166853 A166854 * A166856 A166857 A166858

KEYWORD

nonn

AUTHOR

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

STATUS

approved