A168959 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = 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.

First disagreement at index 22: a(22) = 310248922250956840604217394923586461, A170761(22) = 310248922250956840604217394923587322. - Klaus Brockhaus, Apr 10 2011

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, -820).

Formula

G.f.: (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^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).

Crossrefs

Cf. A170761 (G.f.: (1+x)/(1-41*x)).

Sequence in context: A168815 A168863 A168911 * A169007 A169055 A169103

Adjacent sequences: A168956 A168957 A168958 * A168960 A168961 A168962

Keyword

nonn

Author

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

Status

approved