The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A167922 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A167922

Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.
(history; published version)

#16 by Michael De Vlieger at Wed Sep 13 08:49:42 EDT 2023

STATUS

reviewed

approved

#15 by Joerg Arndt at Wed Sep 13 03:42:17 EDT 2023

STATUS

proposed

reviewed

#14 by G. C. Greubel at Wed Sep 13 03:35:39 EDT 2023

STATUS

editing

proposed

#13 by G. C. Greubel at Wed Sep 13 03:35:07 EDT 2023

LINKS

<a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, -78).

FORMULA

From G. C. Greubel, Sep 13 2023: (Start)

G.f.: (1+t)*(1-t^16)/(1 - 13*t + 90*t^16 - 78*t^17).

a(n) = 12*Sum_{j=1..15} a(n-j) - 78*a(n-16). (End)

MATHEMATICA

CoefficientList[Series[(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)/(78*t^16 - 12*t^15 - 12*t^14 - 12*t^13 - 12*t^12 - 12*t^11 - 12*t^10 - 12*t^9 - 12*t^8 - 12*t^7 - 12*t^6 - 12*t^5 - 12*t^4 - 12*t^3 - 12*t^2 - 12*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Jul 01 2016 *)

CoefficientList[Series[(1+t)*(1-t^16)/(1-13*t+90*t^16-78*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 01 2016; Sep 13 2023 *)

coxG[{16, 78, -12, 40}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 13 2023 *)

PROG

(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-13*x+90*x^16-78*x^17) )); // G. C. Greubel, Sep 13 2023

(SageMath)

def A167922_list(prec):

P.<x> = PowerSeriesRing(ZZ, prec)

return P( (1+x)*(1-x^16)/(1-13*x+90*x^16-78*x^17) ).list()

A167922_list(40) # G. C. Greubel, Sep 13 2023

CROSSREFS

Cf. A154638, A169452, A170733.

Cf. A167881, A167882, A167896 - A167900, A167908, A167914, A167916, A167919, A167923, A167924, A167926, A167927, A167929, A167931, A167933, A167935, A167937, A167938, A167940 - A167947, A167949 - A167962, A167978, A167980, A167988, A167989.

STATUS

approved

editing

#12 by Ray Chandler at Thu Nov 24 12:36:47 EST 2016

STATUS

editing

approved

#11 by Ray Chandler at Thu Nov 24 12:36:45 EST 2016

LINKS

<a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, -78).

STATUS

approved

editing

#10 by N. J. A. Sloane at Fri Jul 01 23:55:33 EDT 2016

STATUS

reviewed

approved

#9 by Wesley Ivan Hurt at Fri Jul 01 22:38:18 EDT 2016

STATUS

proposed

reviewed

#8 by Wesley Ivan Hurt at Fri Jul 01 22:38:14 EDT 2016

STATUS

editing

proposed

#7 by Wesley Ivan Hurt at Fri Jul 01 22:38:07 EDT 2016

CROSSREFS

Cf. A154638, A170733.

STATUS

proposed

editing