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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. 1

%I

%S 2,6,22,78,272,940,3232,11080,37920,129648,443008,1513248,5168000,

%T 17647552,60258304,205746304,702484992,2398480128,8189016064,

%U 27959235072,95459170304,325918735360,1112757649408,3799195224064

%N 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.

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

%D 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.

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

%e 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.

%p 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);

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

%Y Cf. A181365

%K nonn

%O 1,1

%A _Emeric Deutsch_, Oct 15 2010

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Last modified August 12 08:33 EDT 2020. Contains 336438 sequences. (Running on oeis4.)