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A181337
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Number of even entries in the top rows of 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.
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3
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0, 1, 6, 28, 123, 512, 2064, 8124, 31416, 119820, 451972, 1689532, 6268276, 23107836, 84721796, 309151932, 1123431812, 4067533244, 14679173444, 52821023932, 189571527236, 678748381372, 2424976195396, 8646702275772
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OFFSET
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0,3
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COMMENTS
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For the case of the odd entries see A181336.
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REFERENCES
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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.
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LINKS
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FORMULA
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G.f. = z(1+z-z^2)(1-z)^2/[(1+z)(1-4z+2z^2)^2].
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EXAMPLE
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a(2)=6 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=6 even entries.
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MAPLE
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g := z*(1-z)^2*(1+z-z^2)/((1+z)*(1-4*z+2*z^2)^2): gser := series(g, z = 0, 28): seq(coeff(gser, z, n), n = 0 .. 25);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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