A170051 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = 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, -820).

Formula

G.f. (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^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[{36, 820, -40}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 07 2024 *)

Crossrefs

Sequence in context: A169487 A169535 A170003 * A170099 A170147 A170195

Adjacent sequences: A170048 A170049 A170050 * A170052 A170053 A170054

Keyword

nonn

Author

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

Status

approved