A181326 Number of columns with an odd sum 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, 2, 8, 40, 168, 696, 2776, 10864, 41800, 158816, 597176, 2226512, 8242344, 30328160, 111013784, 404518640, 1468154504, 5309771264, 19143323000, 68823556368, 246805713000, 883028659744, 3152718627672, 11234773009200

Offset

0,2

Comments

a(n)=Sum(A181308(n,k), k=0..n).

For the "even sum" case, see A181328.

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 (6,-5,-16,8,8,-4).

Formula

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

Example

a(2)=8 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+0+0+2+2+2+2=8 columns with odd sums.

Maple

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

Crossrefs

Cf. A181308, A181327, A181328

Sequence in context: A366478 A074092 A003445 * A220964 A231125 A221587

Adjacent sequences: A181323 A181324 A181325 * A181327 A181328 A181329

Keyword

nonn,easy

Author

Emeric Deutsch, Oct 13 2010

Status

approved