A170575 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = 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, 36, 36, -666).

Formula

G.f. (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)/(666*t^47 -

36*t^46 - 36*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[{47, 666, -36}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 13 2018 *)

Crossrefs

Sequence in context: A170431 A170479 A170527 * A170623 A170671 A170719

Adjacent sequences: A170572 A170573 A170574 * A170576 A170577 A170578

Keyword

nonn

Author

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

Status

approved