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 A169452 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I. 920
 1, 7, 42, 252, 1512, 9072, 54432, 326592, 1959552, 11757312, 70543872, 423263232, 2539579392, 15237476352, 91424858112, 548549148672, 3291294892032, 19747769352192, 118486616113152, 710919696678912, 4265518180073472 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The initial terms coincide with those of A003949, although the two sequences are eventually different. Computed with MAGMA using commands similar to those used to compute A154638. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, -15). FORMULA G.f.: (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)/(15*t^33 - 5*t^32 - 5*t^31 - 5*t^30 - 5*t^29 - 5*t^28 - 5*t^27 - 5*t^26 - 5*t^25 - 5*t^24 - 5*t^23 - 5*t^22 - 5*t^21 - 5*t^20 - 5*t^19 - 5*t^18 - 5*t^17 - 5*t^16 - 5*t^15 - 5*t^14 - 5*t^13 - 5*t^12 - 5*t^11 - 5*t^10 - 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1). G.f.: (1+x)*(1-x^33)/(1 - 6*x + 20*x^33 - 15*x^34). - G. C. Greubel, May 01 2019 a(n) = -15*a(n-33) + 5*Sum_{k=1..32} a(n-k). - Wesley Ivan Hurt, May 06 2021 MAPLE gf:= (t+1) *(t^2+t+1) *(t^10+t^9+t^8+t^7+t^6+t^5+t^4+t^3+t^2+t+1) *(t^20-t^19+t^17-t^16 +t^14-t^13+t^11-t^10+t^9-t^7+t^6-t^4+t^3- t+1) / (15*t^33-5*t^32-5*t^31-5*t^30-5*t^29 -5*t^28-5*t^27 -5*t^26-5*t^25 -5*t^24 -5*t^23-5*t^22-5*t^21-5*t^20 -5*t^19-5*t^18-5*t^17 -5*t^16 -5*t^15 -5*t^14-5*t^13-5*t^12-5*t^11-5*t^10-5*t^9-5*t^8-5*t^7 -5*t^6 -5*t^5-5*t^4 -5*t^3-5*t^2-5*t+1): S:= series(gf, t, 101): seq(coeff(S, t, j), j=0..100); # Robert Israel, Aug 26 2014 MATHEMATICA coxG[{pwr_, c1_, c2_, trms_:20}]:=Module[{num=Total[2t^Range[pwr-1]]+t^pwr+ 1, den =Total[c2*t^Range[pwr-1]]+c1*t^pwr+1}, CoefficientList[ Series[ num/den, {t, 0, trms}], t]]; coxG[{33, 15, -5, 30}] (* "pwr" is the largest exponent in the g.f.; "c1" is the first coefficient in the denominator of the g.f.; "c2" is the second coefficient in the denominator of the g.f.; "trms" is the number of terms desired (with a default number of 20) *) (* Harvey P. Dale, Aug 16 2014 *) CoefficientList[Series[(1+x)*(1-x^33)/(1-6*x+20*x^33-15*x^34), {x, 0, 25}], x] (* G. C. Greubel, May 01 2019 *) PROG (PARI) my(x='x+O('x^25)); Vec((1+x)*(1-x^33)/(1-6*x+20*x^33-15*x^34)) \\ G. C. Greubel, May 01 2019 (MAGMA) R:=PowerSeriesRing(Integers(), 25); Coefficients(R!( (1+x)*(1-x^3)/(1-14*x+104*x^3-91*x^4) )); // G. C. Greubel, May 01 2019 (Sage) ((1+x)*(1-x^33)/(1-6*x+20*x^33-15*x^34)).series(x, 25).coefficients(x, sparse=False) # G. C. Greubel, May 01 2019 CROSSREFS Sequence in context: A169308 A169356 A169404 * A169500 A169548 A170016 Adjacent sequences:  A169449 A169450 A169451 * A169453 A169454 A169455 KEYWORD nonn,easy AUTHOR John Cannon and N. J. A. Sloane, Dec 03 2009 STATUS approved

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Last modified July 26 13:40 EDT 2021. Contains 346294 sequences. (Running on oeis4.)