A170645 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.

1, 12, 132, 1452, 15972, 175692, 1932612, 21258732, 233846052, 2572306572, 28295372292, 311249095212, 3423740047332, 37661140520652, 414272545727172, 4556998002998892, 50126978032987812, 551396758362865932

Offset

0,2

Comments

The initial terms coincide with those of A003954, 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..200

Index entries for linear recurrences with constant coefficients, signature (10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, -55).

Formula

G.f. (t^49 + 2*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)/(55*t^49 - 10*t^48 - 10*t^47 - 10*t^46 - 10*t^45 - 10*t^44 - 10*t^43

- 10*t^42 - 10*t^41 - 10*t^40 - 10*t^39 - 10*t^38 - 10*t^37 - 10*t^36 -

10*t^35 - 10*t^34 - 10*t^33 - 10*t^32 - 10*t^31 - 10*t^30 - 10*t^29 -

10*t^28 - 10*t^27 - 10*t^26 - 10*t^25 - 10*t^24 - 10*t^23 - 10*t^22 -

10*t^21 - 10*t^20 - 10*t^19 - 10*t^18 - 10*t^17 - 10*t^16 - 10*t^15 -

10*t^14 - 10*t^13 - 10*t^12 - 10*t^11 - 10*t^10 - 10*t^9 - 10*t^8 -

10*t^7 - 10*t^6 - 10*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1)

Mathematica

With[{num=Total[2t^Range[48]]+t^49+1, den=Total[-10 t^Range[48]]+55t^49+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Jul 19 2014 *)

Crossrefs

Sequence in context: A170501 A170549 A170597 * A170693 A120673 A120674

Adjacent sequences: A170642 A170643 A170644 * A170646 A170647 A170648

Keyword

nonn

Author

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

Status

approved