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 A164664 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I. 2
 1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773314, 292889869272, 7908026195160, 213516699839352, 5764950695053368, 155653663349994264, 4202648764205784984, 113471512684966713186, 3063730735882188973692 (list; graph; refs; listen; history; text; internal format)
 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 G. C. Greubel, Table of n, a(n) for n = 0..695 Index entries for linear recurrences with constant coefficients, signature (26,26,26,26,26,26,-351). FORMULA G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(351*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1). MAPLE seq(coeff(series((1+t)*(1-t^7)/(1-27*t+377*t^7-351*t^8), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Sep 15 2019 MATHEMATICA CoefficientList[Series[(t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(351*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1), {t, 0, 20}], t] (* Wesley Ivan Hurt, Apr 25 2017 *) coxG[{7, 351, -26}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 13 2018 *) PROG (PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^7)/(1-27*t+377*t^7-351*t^8)) \\ G. C. Greubel, Sep 15 2019 (MAGMA) R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^7)/(1-27*t+377*t^7-351*t^8) )); // G. C. Greubel, Sep 15 2019 (Sage) def A164664_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P((1+t)*(1-t^7)/(1-27*t+377*t^7-351*t^8)).list() A164664_list(20) # G. C. Greubel, Sep 15 2019 (GAP) a:=[28, 756, 20412, 551124, 14880348, 401769396, 10847773314];; for n in [8..30] do a[n]:=26*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]+a[n-6]) -351*a[n-7]; od; Concatenation([1], a); # G. C. Greubel, Sep 15 2019 CROSSREFS Cf. A154638, A170747. Sequence in context: A163187 A163548 A164025 * A164970 A165456 A165980 Adjacent sequences:  A164661 A164662 A164663 * A164665 A164666 A164667 KEYWORD nonn AUTHOR John Cannon and N. J. A. Sloane, Dec 03 2009 STATUS approved

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Last modified July 31 22:32 EDT 2021. Contains 346377 sequences. (Running on oeis4.)