A181305 Number of increasing columns in all 2-compositions of 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

Author

Emeric Deutsch, Oct 13 2010

Keywords

• nonn
• easy

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 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.

For the case of the even entries see A181337.

Examples

			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.
		

Links

• G. Castiglione, A. Frosini, E. Munarini, A. Restivo and S. Rinaldi, Combinatorial aspects of L-convex polyominoes, European J. Combin. 28 (2007), no. 6, 1724-1741.
• Index entries for linear recurrences with constant coefficients, signature (7,-12,-4,12,-4).

Crossrefs

Cf. A181304, A181337.

Programs

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);

Formula

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

a(n) = Sum_{k=0..n} k*A181304(n,k).

Extensions

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