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

9, 120, 753, 3612, 15040, 57366, 206115, 709152, 2360943, 7659870, 24340184, 76031100, 234116493, 712166952, 2143779645, 6394719216, 18923041360, 55601888562, 162350117703, 471371537040, 1361642740059

Offset: 0

Author

Wolfdieter Lang, Apr 20 2001

Keywords

• nonn
• easy

Comments

Numerator of g.f. is row polynomial Sum_{m=0..4} A061187(2,m)*x^m.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-30,45,-30,9,-1).

Crossrefs

Cf. A002548, 2*A061171.

Programs

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

Mathematica

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 *)

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

Formula

a(n) = A060924(n+2, 2).

G.f.: (3-2*x)*(4*x^3-9*x^2+15*x+3)/(1-3*x+x^2)^3.