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, 56375692407808, 200307512532992, 710622022258688, 2517475213557760

Offset: 0

Author

Emeric Deutsch, Oct 12 2010

Keywords

• nonn
• easy

Links

• 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.
• Index entries for linear recurrences with constant coefficients, signature (8,-20,16,-4).

Crossrefs

Cf. A181289.

Programs

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);

Formula

a(n) = Sum_{k=0..n} k * A181289(n,k).

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