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A181331
Number of 0's in the top rows of all 2-compositions of n.
2
0, 1, 5, 23, 99, 408, 1632, 6388, 24596, 93488, 351664, 1311536, 4856432, 17873408, 65436544, 238480960, 865665600, 3131196672, 11290210560, 40594476800, 145588087552, 520933746688, 1860059009024, 6628828632064, 23582036472832
OFFSET
0,3
COMMENTS
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.
LINKS
G. Castiglione, A. Frosini, E. Munarini, A. Restivo and S. Rinaldi, Combinatorial aspects of L-convex polyominoes, European J. Combin. 28 (2007), no. 6, 1724-1741.
FORMULA
a(n) = Sum_{k=0..n} A181330(n,k).
a(n) = (1/2)*A181294(n).
G.f.: x*(1 - x)^3 / (1 - 4*x + 2*x^2)^2.
a(n) = A181292(n)-2*A181292(n-1)+A181292(n-2). - R. J. Mathar, Jul 24 2022
EXAMPLE
a(2)=5 because in (0/2), (1/1), (2,0), (1,0/0,1), (0,1/1,0), (1,1/0,0), and (0,0/1,1) (the 2-compositions are written as (top row / bottom row)) we have 1+0+1+1+1+0+2=5 zeros.
MAPLE
g := z*(1-z)^3/(1-4*z+2*z^2)^2: gser := series(g, z = 0, 30): seq(coeff(gser, z, n), n = 0 .. 27);
MATHEMATICA
LinearRecurrence[{8, -20, 16, -4}, {0, 1, 5, 23, 99}, 25] (* Georg Fischer, Feb 01 2021 *)
CROSSREFS
Sequence in context: A119012 A215038 A084615 * A268400 A364754 A339232
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Oct 13 2010
STATUS
approved