cp's OEIS Frontend

A061172 Third column of Lucas bisection triangle (odd part).

%I A061172 #10 Feb 29 2024 15:48:59
%S A061172 9,120,753,3612,15040,57366,206115,709152,2360943,7659870,24340184,
%T A061172 76031100,234116493,712166952,2143779645,6394719216,18923041360,
%U A061172 55601888562,162350117703,471371537040,1361642740059
%N A061172 Third column of Lucas bisection triangle (odd part).
%C A061172 Numerator of g.f. is row polynomial Sum_{m=0..4} A061187(2,m)*x^m.
%H A061172 G. C. Greubel, <a href="/A061172/b061172.txt">Table of n, a(n) for n = 0..1000</a>
%H A061172 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (9,-30,45,-30,9,-1).
%F A061172 a(n) = A060924(n+2, 2).
%F A061172 G.f.: (3-2*x)*(4*x^3-9*x^2+15*x+3)/(1-3*x+x^2)^3.
%t A061172 CoefficientList[Series[(3-2*x)*(4*x^3-9*x^2+15*x+3)/(1-3*x+x^2)^3, {x,0,50}], x] (* or *) LinearRecurrence[{9,-30,45,-30,9,-1}, {9, 120, 753, 3612, 15040, 57366}, 30] (* _G. C. Greubel_, Dec 21 2017 *)
%o A061172 (PARI) x='x+O('x^30); Vec((3-2*x)*(4*x^3-9*x^2+15*x+3)/(1-3*x+x^2)^3) \\ _G. C. Greubel_, Dec 21 2017
%o A061172 (Magma) I:=[9, 120, 753, 3612, 15040, 57366]; [n le 6 select I[n] else 9*Self(n-1)-30*Self(n-2)+45*Self(n-3)-30*Self(n-4)+9*Self(n-5) - Self(n-6): n in [1..30]]; // _G. C. Greubel_, Dec 21 2017
%Y A061172 Cf. A002548, 2*A061171.
%K A061172 nonn,easy
%O A061172 0,1
%A A061172 _Wolfdieter Lang_, Apr 20 2001