A181298 The number of even entries in all the 2-compositions of n. A 2-composition of n is a nonnegative matrix with two rows, such that each column has at least one nonzero entry and whose entries sum up to n.

0, 2, 12, 56, 246, 1024, 4128, 16248, 62832, 239640, 903944, 3379064, 12536552, 46215672, 169443592, 618303864, 2246863624, 8135066488, 29358346888, 105642047864, 379143054472, 1357496762744, 4849952390792, 17293404551544

Offset: 0

Author

Emeric Deutsch, Oct 12 2010

Keywords

• nonn
• easy

Comments

a(n)=Sum(k*A181297(n,k),k=0..n).

Examples

			a(2)=12 because in the 2-compositions of 2, namely (1/1),(0/2),(2/0),(1,0/0,1),(0,1/1,0),(1,1/0,0), and (0,0/1,1), we have 0+2+2+2+2+2+2=12 odd entries (the 2-compositions are written as (top row/bottom row)).
		

References

• G. Castiglione, A. Frosini, E. Munarini, A. Restivo and S. Rinaldi, Combinatorial aspects of L-convex polyominoes, European Journal of Combinatorics, 28, 2007, 1724-1741.

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-12,-4,12,-4).

Crossrefs

Cf. A181295, A181296, A181297.

Programs

Maple

g := 2*z*(1-z)^2*(1+z-z^2)/((1+z)*(1-4*z+2*z^2)^2): gser := series(g, z = 0, 30): seq(coeff(gser, z, n), n = 0 .. 25);

Formula

G.f. = 2z(1-z)^2*(1+z-z^2)/[(1+z)(1-4z+2z^2)^2].

a(n) = 2*A181337(n). - R. J. Mathar, Jul 26 2022