A181339 Largest entry in a 2-composition of n, summed over 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.

2, 9, 38, 149, 562, 2066, 7474, 26737, 94900, 334909, 1176842, 4121632, 14397370, 50185498, 174628420, 606755258, 2105552976, 7298685677, 25275876584, 87457546835, 302382185770, 1044756677132, 3607460520006, 12449135054480

Offset

1,1

Comments

a(n)=Sum(A181338(n,k),k=0..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=1..24.

Formula

G.f. for 2-compositions with all entries <= k is h(k,z)=(1-z)^2/(1-4z+2z^2+2z^{k+1}-z^{2k+2}).

G.f. for 2-compositions with largest entry k is f(k,z)=h(k,z)-h(k-1,z).

G.f. = G(z)=Sum(k*f(k,z),k=1..infinity).

Example

a(2)=9 because the 2-compositions of 2, written as (top row / bottom row), are (1 / 1), (0 / 2), (2 / 0), (1,0 / 0,1), (0,1 / 1,0), (1,1 / 0,0), (0,0 / 1,1) and we have 1 + 2 + 2 + 1 + 1 + 1 + 1 = 9.

Maple

h := proc (k) options operator, arrow: (1-z)^2/(1-4*z+2*z^2+2*z^(k+1)-z^(2*k+2)) end proc: f := proc (k) options operator, arrow: simplify(h(k)-h(k-1)) end proc: g := sum(k*f(k), k = 1 .. 50): gser := series(g, z = 0, 30): seq(coeff(gser, z, n), n = 1 .. 25);

Crossrefs

Cf. A181338

Sequence in context: A373908 A026591 A007224 * A291265 A037489 A037569

Adjacent sequences: A181336 A181337 A181338 * A181340 A181341 A181342

Keyword

nonn

Author

Emeric Deutsch, Oct 15 2010

Status

approved