A181290 The sum of the lengths of 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. The length of the 2-composition is the number of columns.

0, 2, 11, 52, 227, 944, 3800, 14944, 57748, 220128, 829968, 3101376, 11502704, 42393088, 155392768, 566918144, 2059768384, 7456496128, 26905720576, 96804463616, 347386161920, 1243665567744, 4442849839104, 15840448094208

Offset

0,2

Comments

a(n)=Sum(k*A181289(n,k), 0<=k<=n).

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 (8,-20,16,-4).

Formula

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

Maple

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

Crossrefs

Cf. A181289

Sequence in context: A134963 A026956 A026986 * A026996 A110308 A027201

Adjacent sequences: A181287 A181288 A181289 * A181291 A181292 A181293

Keyword

nonn

Author

Emeric Deutsch, Oct 12 2010

Status

approved