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

Author

Emeric Deutsch, Oct 12 2010

Keywords

• nonn
• easy

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.

Crossrefs

Cf. A181299.

Programs

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);

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