A181337 Number of even entries in the top rows of all 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, 1, 6, 28, 123, 512, 2064, 8124, 31416, 119820, 451972, 1689532, 6268276, 23107836, 84721796, 309151932, 1123431812, 4067533244, 14679173444, 52821023932, 189571527236, 678748381372, 2424976195396, 8646702275772

Offset: 0

Author

Emeric Deutsch, Oct 14 2010

Keywords

• nonn
• easy

Comments

a(n)=Sum(A181336(n,k), k=0..n).

For the case of the odd entries see A181336.

Examples

			a(2)=6 because in (0/2),(1/1),(2/0),(1,0/0,1),(0,1/1,0),(1,1/0,0), and (0,0/1,1) (the 2-compositions are written as (top row / bottom row)) we have 1+0+1+1+1+0+2=6 even entries.
		

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. A181305, A181336.

Programs

Maple

g := z*(1-z)^2*(1+z-z^2)/((1+z)*(1-4*z+2*z^2)^2): gser := series(g, z = 0, 28): seq(coeff(gser, z, n), n = 0 .. 25);

Formula

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