A181294 - OEIS

%I #4 Jul 24 2022 14:09:31

%S 0,2,10,46,198,816,3264,12776,49192,186976,703328,2623072,9712864,

%T 35746816,130873088,476961920,1731331200,6262393344,22580421120,

%U 81188953600,291176175104,1041867493376,3720118018048,13257657264128

%N 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.

%C a(n)=Sum(A181293(n,k),k=0..n).

%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/(1-4z+2z^2)^2.

%F a(n) = 2*A181331(n). - _Emeric Deutsch_, Oct 13 2010

%e 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.

%p 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);

%Y Cf. A181293

%K nonn,easy

%O 0,2

%A _Emeric Deutsch_, Oct 12 2010