A169305 - OEIS

%I #14 Dec 31 2023 15:50:13

%S 1,4,12,36,108,324,972,2916,8748,26244,78732,236196,708588,2125764,

%T 6377292,19131876,57395628,172186884,516560652,1549681956,4649045868,

%U 13947137604,41841412812,125524238436,376572715308,1129718145924

%N Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.

%C The initial terms coincide with those of A003946, although the two sequences are eventually different.

%C First disagreement at index 30: a(30) = 274521509459526, A003946(30) = 274521509459532. - _Klaus Brockhaus_, Jun 22 2011

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

%H <a href="/index/Rec#order_30">Index entries for linear recurrences with constant coefficients</a>, signature (2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -3).

%F G.f.: (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)/(3*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).

%F a(n) = -3*a(n-30) + 2*Sum_{k=1..29} a(n-k). - _Wesley Ivan Hurt_, Dec 31 2023

%t coxG[{30,3,-2,30}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 18 2022 *)

%Y Cf. A003946 (G.f.: (1+x)/(1-3*x)).

%K nonn

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009