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A170603
Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
0
1, 18, 306, 5202, 88434, 1503378, 25557426, 434476242, 7386096114, 125563633938, 2134581776946, 36287890208082, 616894133537394, 10487200270135698, 178282404592306866, 3030800878069216722, 51523614927176684274
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170737, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
Index entries for linear recurrences with constant coefficients, signature (16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, -136).
FORMULA
G.f. (t^48 + 2*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)/(136*t^48 - 16*t^47 - 16*t^46 - 16*t^45 - 16*t^44 - 16*t^43 - 16*t^42
- 16*t^41 - 16*t^40 - 16*t^39 - 16*t^38 - 16*t^37 - 16*t^36 - 16*t^35 -
16*t^34 - 16*t^33 - 16*t^32 - 16*t^31 - 16*t^30 - 16*t^29 - 16*t^28 -
16*t^27 - 16*t^26 - 16*t^25 - 16*t^24 - 16*t^23 - 16*t^22 - 16*t^21 -
16*t^20 - 16*t^19 - 16*t^18 - 16*t^17 - 16*t^16 - 16*t^15 - 16*t^14 -
16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 -
16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1)
MATHEMATICA
coxG[{48, 136, -16}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 30 2019 *)
CROSSREFS
Sequence in context: A170459 A170507 A170555 * A170651 A170699 A170737
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved