A181305 Number of increasing columns in 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.

0, 1, 5, 24, 104, 432, 1736, 6820, 26332, 100308, 377996, 1411844, 5234428, 19285252, 70670972, 257766212, 936336572, 3388962884, 12226547132, 43983439684, 157814634684, 564917186372, 2017873643708, 7193745818436

Offset

0,3

Comments

Also, number of odd entries in the top rows of 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.

a(n)=Sum(A181304(n,k), k=0..n).

For the case of the even entries see A181337.

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 (7, -12, -4, 12, -4).

Formula

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

Example

a(1)=1 because in the 2-compositions of 1, namely (0/1) and (1/0) we have only one increasing column (the 2-compositions are written as (top row / bottom row).
a(2)=5 because in (0/2),(1/1),(2,0),(1,0/0,1),(0,1/1,0),(1,1/0,0), and (0,0/1,1) (the 2-compositions are written as (top row/bottom row)) we have 0+1+0+1+1+2+0=5 odd entries.

Maple

g := z*(1-z)^2/((1+z)*(1-4*z+2*z^2)^2): gser := series(g, z = 0, 30): seq(coeff(gser, z, k), k = 0 .. 27);

Crossrefs

Cf. A181304, A181337.

Sequence in context: A078820 A291395 A179417 * A046724 A272578 A273622

Adjacent sequences: A181302 A181303 A181304 * A181306 A181307 A181308

Keyword

nonn

Author

Emeric Deutsch, Oct 13 2010

Extensions

Edited by N. J. A. Sloane, Oct 15 2010

Status

approved