A170648 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.

1, 15, 210, 2940, 41160, 576240, 8067360, 112943040, 1581202560, 22136835840, 309915701760, 4338819824640, 60743477544960, 850408685629440, 11905721598812160, 166680102383370240, 2333521433367183360

Offset

0,2

Comments

The initial terms coincide with those of A170734, 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..16.

Index entries for linear recurrences with constant coefficients, signature (13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, -91).

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)/(91*t^49 - 13*t^48 - 13*t^47 - 13*t^46 - 13*t^45 - 13*t^44 - 13*t^43

- 13*t^42 - 13*t^41 - 13*t^40 - 13*t^39 - 13*t^38 - 13*t^37 - 13*t^36 -

13*t^35 - 13*t^34 - 13*t^33 - 13*t^32 - 13*t^31 - 13*t^30 - 13*t^29 -

13*t^28 - 13*t^27 - 13*t^26 - 13*t^25 - 13*t^24 - 13*t^23 - 13*t^22 -

13*t^21 - 13*t^20 - 13*t^19 - 13*t^18 - 13*t^17 - 13*t^16 - 13*t^15 -

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

13*t^7 - 13*t^6 - 13*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1).

a(n) = -91*a(n-49) + 13*Sum_{k=1..48} a(n-k). - Wesley Ivan Hurt, May 04 2024

Mathematica

coxG[{49, 91, -13}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 24 2024 *)

Crossrefs

Sequence in context: A170504 A170552 A170600 * A170696 A170734 A186231

Adjacent sequences: A170645 A170646 A170647 * A170649 A170650 A170651

Keyword

nonn

Author

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

Status

approved