A181328 Number of columns with an even 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, 0, 3, 12, 59, 248, 1024, 4080, 15948, 61312, 232792, 874864, 3260360, 12064928, 44378984, 162399504, 591613880, 2146724864, 7762397576, 27980907248, 100580448920, 360636908000, 1290131211432, 4605675085008, 16410645183928

Offset: 0

Author

Emeric Deutsch, Oct 13 2010

Keywords

• nonn

Comments

a(n)=Sum(A181327(n,k), k>=0).

Examples

			a(2)=3 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 1+1+1+0+0+0+0=3 columns with even sums.
		

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

• Index entries for linear recurrences with constant coefficients, signature (6,-5,-16,8,8,-4).

Crossrefs

Cf. A181327, A181326

Programs

Maple

g := z^2*(1-z)^2*(3-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);

Formula

G.f. = z^2*(1-z)^2*(3-z^2)/[(1+z)(1-4z+2z^2)]^2.

a(n) = (3*A181326(n-1) -A181326(n-3))/2. - R. J. Mathar, Jul 24 2022