A170291 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.

1, 42, 1722, 70602, 2894682, 118681962, 4865960442, 199504378122, 8179679503002, 335366859623082, 13750041244546362, 563751691026400842, 23113819332082434522, 947666592615379815402, 38854330297230572431482

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

Table of n, a(n) for n=0..14.

Index entries for linear recurrences with constant coefficients, signature (40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, -820).

Formula

G.f. (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)/(820*t^41 - 40*t^40 - 40*t^39 - 40*t^38 - 40*t^37 - 40*t^36 - 40*t^35

- 40*t^34 - 40*t^33 - 40*t^32 - 40*t^31 - 40*t^30 - 40*t^29 - 40*t^28 -

40*t^27 - 40*t^26 - 40*t^25 - 40*t^24 - 40*t^23 - 40*t^22 - 40*t^21 -

40*t^20 - 40*t^19 - 40*t^18 - 40*t^17 - 40*t^16 - 40*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

coxG[{41, 820, -40}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 19 2014 *)

Crossrefs

Sequence in context: A170147 A170195 A170243 * A170339 A170387 A170435

Adjacent sequences: A170288 A170289 A170290 * A170292 A170293 A170294

Keyword

nonn

Author

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

Status

approved