A181294 Number of 0's 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, 10, 46, 198, 816, 3264, 12776, 49192, 186976, 703328, 2623072, 9712864, 35746816, 130873088, 476961920, 1731331200, 6262393344, 22580421120, 81188953600, 291176175104, 1041867493376, 3720118018048, 13257657264128

Offset

0,2

Comments

a(n)=Sum(A181293(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.

Formula

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

a(n) = 2*A181331(n). - Emeric Deutsch, Oct 13 2010

Example

a(2)=10 because the 2-compositions of 2, written as (top row / bottom row), are (1/1),(0/2),(2/0),(1,0/0,1),(0,1/1,0),(1,1/0,0),(0,0/1,1), having 0 + 1 + 1 + 2 + 2 + 2 + 2 = 10 zeros.

Maple

g := 2*z*(1-z)^3/(1-4*z+2*z^2)^2: gser := series(g, z = 0, 30): seq(coeff(gser, z, n), n = 0 .. 25);

Crossrefs

Cf. A181293

Sequence in context: A212387 A191813 A360412 * A080643 A032389 A290923

Adjacent sequences: A181291 A181292 A181293 * A181295 A181296 A181297

Keyword

nonn,easy

Author

Emeric Deutsch, Oct 12 2010

Status

approved