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A170613
Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
0
1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579636, 5764951698650172, 155653695863554644, 4202649788315975388, 113471544284531335476, 3063731695682346057852
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170747, 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 (26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, -351).
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)/(351*t^48 - 26*t^47 - 26*t^46 - 26*t^45 - 26*t^44 - 26*t^43 - 26*t^42
- 26*t^41 - 26*t^40 - 26*t^39 - 26*t^38 - 26*t^37 - 26*t^36 - 26*t^35 -
26*t^34 - 26*t^33 - 26*t^32 - 26*t^31 - 26*t^30 - 26*t^29 - 26*t^28 -
26*t^27 - 26*t^26 - 26*t^25 - 26*t^24 - 26*t^23 - 26*t^22 - 26*t^21 -
26*t^20 - 26*t^19 - 26*t^18 - 26*t^17 - 26*t^16 - 26*t^15 - 26*t^14 -
26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 -
26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1)
MATHEMATICA
coxG[{48, 351, -26}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Feb 24 2023 *)
CROSSREFS
Sequence in context: A170469 A170517 A170565 * A170661 A170709 A170747
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved