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A167848 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^15 = I. 1
1, 42, 1722, 70602, 2894682, 118681962, 4865960442, 199504378122, 8179679503002, 335366859623082, 13750041244546362, 563751691026400842, 23113819332082434522, 947666592615379815402, 38854330297230572431482 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170761, 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 (40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, -820).

FORMULA

G.f.: (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)/(820*t^15 - 40*t^14 - 40*t^13 - 40*t^12 - 40*t^11 - 40*t^10 - 40*t^9 - 40*t^8 - 40*t^7 - 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 - 40*t + 1).

MATHEMATICA

CoefficientList[Series[(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)/(820*t^15 - 40*t^14 - 40*t^13 - 40*t^12 - 40*t^11 - 40*t^10 - 40*t^9 - 40*t^8 - 40*t^7 - 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 - 40*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Jun 28 2016 *)

CROSSREFS

Sequence in context: A170579 A170627 A170675 A170723 A170761 A218744 A158727

Adjacent sequences:  A167845 A167846 A167847 * A167849 A167850 A167851

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified February 17 23:47 EST 2018. Contains 299297 sequences. (Running on oeis4.)