A181301 Number of 2-compositions of n having no column with equal entries. 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.

1, 2, 6, 20, 64, 206, 662, 2128, 6840, 21986, 70670, 227156, 730152, 2346942, 7543822, 24248256, 77941648, 250529378, 805281526, 2588432308, 8320049072, 26743297998, 85961510758, 276307781200, 888141556360, 2854770939522

Offset

0,2

Comments

a(n)=A181299(n,0).

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..25.

Formula

G.f. = (1+z)(1-z)^2/(1-3z-z^2+z^3).

a(n) = Sum_{k, 0<=k<=n} A060086(n,k)*2^k. - Philippe Deléham, Feb 24 2012

a(n) = 2*A033505(n-1), n>0. - R. J. Mathar, Jul 24 2022

Maple

g := (1+z)*(1-z)^2/(1-3*z-z^2+z^3): gser := series(g, z = 0, 30): seq(coeff(gser, z, n), n = 0 .. 27);

Crossrefs

Cf. A181299.

Sequence in context: A053730 A220874 A273902 * A302612 A005726 A148473

Adjacent sequences: A181298 A181299 A181300 * A181302 A181303 A181304

Keyword

nonn,easy

Author

Emeric Deutsch, Oct 12 2010

Status

approved