A163093 - OEIS

A163093

Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

1, 17, 272, 4352, 69496, 1109760, 17721480, 282988800, 4518961080, 72161899200, 1152331158600, 18401221627200, 293843444945400, 4692295538064000, 74929823330517000, 1196531288107632000, 19107039891249747000, 305114439575750760000, 4872278582526960045000

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OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170736, although the two sequences are eventually different.

Computed with Magma using commands similar to those used to compute A154638.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..831

Index entries for linear recurrences with constant coefficients, signature (15,15,15,-120).

FORMULA

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(120*t^4 - 15*t^3 - 15*t^2 - 15*t + 1).

MATHEMATICA

CoefficientList[Series[(t^4 + 2 t^3 + 2 t^2 + 2 t + 1)/(120 t^4 - 15 t^3 - 15 t^2 - 15 t + 1), {t, 0, 20}], t] (* Jinyuan Wang, Mar 23 2020 *)

(* Alternative: *)

coxG[{4, 120, -15}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 06 2026 *)

(* Alternative: *)

LinearRecurrence[{15, 15, 15, -120}, {1, 17, 272, 4352, 69496}, 20] (* Harvey P. Dale, Aug 06 2026 *)

PROG

(PARI) a(n)=if(n, ([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -120, 15, 15, 15]^(n-1)*[17; 272; 4352; 69496])[1, 1], 1) \\ Charles R Greathouse IV, Aug 14 2026

CROSSREFS

Cf. A170736, A154638.

Sequence in context: A159678 A162803 A097830 * A163451 A163965 A164628

Adjacent sequences: A163090 A163091 A163092 * A163094 A163095 A163096

KEYWORD

nonn,easy

AUTHOR

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

EXTENSIONS

More terms from Jinyuan Wang, Mar 23 2020

STATUS

approved