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A181331
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Number of 0's in the top rows of all 2-compositions of n.
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2
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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
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OFFSET
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0,3
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COMMENTS
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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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LINKS
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FORMULA
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G.f.: x*(1 - x)^3 / (1 - 4*x + 2*x^2)^2.
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EXAMPLE
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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.
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MAPLE
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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);
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MATHEMATICA
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LinearRecurrence[{8, -20, 16, -4}, {0, 1, 5, 23, 99}, 25] (* Georg Fischer, Feb 01 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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