A181367 Number of 2-compositions of n containing at least one 0 entry. 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.

2, 6, 22, 78, 272, 940, 3232, 11080, 37920, 129648, 443008, 1513248, 5168000, 17647552, 60258304, 205746304, 702484992, 2398480128, 8189016064, 27959235072, 95459170304, 325918735360, 1112757649408, 3799195224064

Offset

1,1

Comments

a(n)=A181365(n,0).

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=1..24.

Index entries for linear recurrences with constant coefficients, signature (6,-10,4).

Formula

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

4*a(n) = 2*A007070(n)-2^n, n>1. - R. J. Mathar, Jul 22 2022

Example

a(2)=6 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) and only the first one does not contain a 0 entry.

Maple

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

Mathematica

CoefficientList[Series[(2x (1-x)^3)/((1-2x)(1-4x+2x^2)), {x, 0, 30}], x] (* Harvey P. Dale, Mar 29 2020 *)

Crossrefs

Cf. A181365

Sequence in context: A262068 A148496 A217528 * A106434 A150228 A203038

Adjacent sequences: A181364 A181365 A181366 * A181368 A181369 A181370

Keyword

nonn,easy

Author

Emeric Deutsch, Oct 15 2010

Status

approved