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

0,3

Comments

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

For the case of the odd entries see A181336.

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

Table of n, a(n) for n=0..23.

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

Formula

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

Example

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.

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);

Crossrefs

Cf. A181305, A181336.

Sequence in context: A026851 A267689 A300996 * A002693 A289779 A376969

Adjacent sequences: A181334 A181335 A181336 * A181338 A181339 A181340

Keyword

nonn,easy

Author

Emeric Deutsch, Oct 14 2010

Status

approved