A170479 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.

1, 38, 1406, 52022, 1924814, 71218118, 2635070366, 97497603542, 3607411331054, 133474219248998, 4938546112212926, 182726206151878262, 6760869627619495694, 250152176221921340678, 9255630520211089605086

Offset

0,2

Comments

The initial terms coincide with those of A170757, 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 (36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, -666).

Formula

G.f. (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)/(666*t^45 - 36*t^44 - 36*t^43 -

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

36*t^35 - 36*t^34 - 36*t^33 - 36*t^32 - 36*t^31 - 36*t^30 - 36*t^29 -

36*t^28 - 36*t^27 - 36*t^26 - 36*t^25 - 36*t^24 - 36*t^23 - 36*t^22 -

36*t^21 - 36*t^20 - 36*t^19 - 36*t^18 - 36*t^17 - 36*t^16 - 36*t^15 -

36*t^14 - 36*t^13 - 36*t^12 - 36*t^11 - 36*t^10 - 36*t^9 - 36*t^8 -

36*t^7 - 36*t^6 - 36*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1)

Mathematica

coxG[{45, 666, -36}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 20 2016 *)

Crossrefs

Sequence in context: A170335 A170383 A170431 * A170527 A170575 A170623

Adjacent sequences: A170476 A170477 A170478 * A170480 A170481 A170482

Keyword

nonn

Author

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

Status

approved