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A166468 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I. 2
1, 4, 12, 36, 108, 324, 972, 2916, 8748, 26244, 78732, 236196, 708582, 2125728, 6377136, 19131264, 57393360, 172178784, 516532464, 1549585728, 4648722192, 13946061600, 41837869872, 125512664832, 376535160174, 1129596977628 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A003946, although the two sequences are eventually different.

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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -3).

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)/(3*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).

MATHEMATICA

CoefficientList[Series[(x^12 + 2 x^11 + 2 x^10 + 2 x^9 + 2 x^8 + 2 x^7 + 2 x^6 + 2 x^5 + 2 x^4 + 2 x^3 + 2 x^2 + 2 x + 1)/(3 x^12 - 2 x^11 - 2 x^10 - 2 x^9 - 2 x^8 - 2 x^7 - 2 x^6 - 2 x^5 - 2 x^4 - 2 x^3 - 2 x^2 - 2 x + 1), {x, 0, 40}], x ] (* Vincenzo Librandi, Apr 29 2014 *)

CROSSREFS

Sequence in context: A165184 A165756 A166328 * A166858 A167105 A167649

Adjacent sequences:  A166465 A166466 A166467 * A166469 A166470 A166471

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified June 22 07:47 EDT 2017. Contains 288605 sequences.