cp's OEIS Frontend

A169222 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.

%I A169222 #14 Mar 01 2023 15:39:42
%S A169222 1,17,272,4352,69632,1114112,17825792,285212672,4563402752,
%T A169222 73014444032,1168231104512,18691697672192,299067162755072,
%U A169222 4785074604081152,76561193665298432,1224979098644774912,19599665578316398592
%N A169222 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
%C A169222 The initial terms coincide with those of A170736, although the two sequences are eventually different.
%C A169222 First disagreement at index 28: a(28) = 5516815412193254355313652349796216, A170736(28) = 5516815412193254355313652349796352. - _Klaus Brockhaus_, May 24 2011
%C A169222 Computed with Magma using commands similar to those used to compute A154638.
%H A169222 <a href="/index/Rec#order_28">Index entries for linear recurrences with constant coefficients</a>, signature (15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, -120).
%F A169222 G.f.: (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)/(120*t^28 - 15*t^27 - 15*t^26 - 15*t^25 - 15*t^24 - 15*t^23 - 15*t^22 - 15*t^21 - 15*t^20 - 15*t^19 - 15*t^18 - 15*t^17 - 15*t^16 - 15*t^15 - 15*t^14 - 15*t^13 - 15*t^12 - 15*t^11 - 15*t^10 - 15*t^9 - 15*t^8 - 15*t^7 - 15*t^6 - 15*t^5 - 15*t^4 - 15*t^3 - 15*t^2 - 15*t + 1).
%F A169222 a(n) = -120*a(n-28) + 15*Sum_{k=1..27} a(n-k). - _Wesley Ivan Hurt_, Mar 01 2023
%t A169222 coxG[{28,120,-15}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 12 2019 *)
%Y A169222 Cf. A170736 (G.f.: (1+x)/(1-16*x)).
%K A169222 nonn
%O A169222 0,2
%A A169222 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009