A181298 The number of even entries in all the 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, 12, 56, 246, 1024, 4128, 16248, 62832, 239640, 903944, 3379064, 12536552, 46215672, 169443592, 618303864, 2246863624, 8135066488, 29358346888, 105642047864, 379143054472, 1357496762744, 4849952390792, 17293404551544

Offset

0,2

Comments

a(n)=Sum(k*A181297(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=0..23.

Index entries for linear recurrences with constant coefficients, signature (7,-12,-4,12,-4).

Formula

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

a(n) = 2*A181337(n). - R. J. Mathar, Jul 26 2022

Example

a(2)=12 because in the 2-compositions of 2, namely (1/1),(0/2),(2/0),(1,0/0,1),(0,1/1,0),(1,1/0,0), and (0,0/1,1), we have 0+2+2+2+2+2+2=12 odd entries (the 2-compositions are written as (top row/bottom row)).

Maple

g := 2*z*(1-z)^2*(1+z-z^2)/((1+z)*(1-4*z+2*z^2)^2): gser := series(g, z = 0, 30): seq(coeff(gser, z, n), n = 0 .. 25);

Crossrefs

Cf. A181295, A181296, A181297.

Sequence in context: A127221 A020522 A037130 * A247121 A078543 A084128

Adjacent sequences: A181295 A181296 A181297 * A181299 A181300 A181301

Keyword

nonn,easy

Author

Emeric Deutsch, Oct 12 2010

Status

approved