A061169 Third column of Lucas bisection triangle (even part).

1, 39, 315, 1687, 7470, 29634, 109421, 384105, 1298613, 4264835, 13686456, 43102644, 133636825, 408900987, 1237114335, 3706490479, 11010661266, 32463981270, 95081107013, 276820695645, 801633669561

Offset: 0

Author

Wolfdieter Lang, Apr 20 2001

Keywords

• nonn
• easy

Comments

Numerator of g.f. is row polynomial Sum_{m=0..4} A061186(3,m)*x^m.

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..2374
• Geoffrey B. Campbell, Vector Partition Identities for 2D, 3D and nD Lattices, arXiv:2302.01091 [math.CO], 2023.

Crossrefs

A002878(n)=A060923(n, 0), A060934.

Programs

Mathematica

CoefficientList[Series[(1 + x) (1 + 29 x - 35 x^2 + 12 x^3)/(1 - 3 x + x^2)^3, {x, 0, 20}], x] (* Michael De Vlieger, Feb 06 2023 *)

Formula

a(n) = A060923(n+2, 2).

G.f.: (1+x)*(1+29*x-35*x^2+12*x^3)/(1-3*x+x^2)^3.