A170522 - OEIS

A170522

Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.

1, 33, 1056, 33792, 1081344, 34603008, 1107296256, 35433480192, 1133871366144, 36283883716608, 1161084278931456, 37154696925806592, 1188950301625810944, 38046409652025950208, 1217485108864830406656, 38959523483674573012992

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OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170752, 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..15.

Index entries for linear recurrences with constant coefficients, signature (31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, -496).

FORMULA

G.f. (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)/(496*t^46 - 31*t^45 -

31*t^44 - 31*t^43 - 31*t^42 - 31*t^41 - 31*t^40 - 31*t^39 - 31*t^38 -

31*t^37 - 31*t^36 - 31*t^35 - 31*t^34 - 31*t^33 - 31*t^32 - 31*t^31 -

31*t^30 - 31*t^29 - 31*t^28 - 31*t^27 - 31*t^26 - 31*t^25 - 31*t^24 -

31*t^23 - 31*t^22 - 31*t^21 - 31*t^20 - 31*t^19 - 31*t^18 - 31*t^17 -

31*t^16 - 31*t^15 - 31*t^14 - 31*t^13 - 31*t^12 - 31*t^11 - 31*t^10 -

31*t^9 - 31*t^8 - 31*t^7 - 31*t^6 - 31*t^5 - 31*t^4 - 31*t^3 - 31*t^2 -

31*t + 1)

MATHEMATICA

coxG[{46, 496, -31}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 19 2019 *)

CROSSREFS

Sequence in context: A170378 A170426 A170474 * A170570 A170618 A170666

Adjacent sequences: A170519 A170520 A170521 * A170523 A170524 A170525

KEYWORD

nonn

AUTHOR

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

STATUS

approved