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A181367
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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.
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1
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2, 6, 22, 78, 272, 940, 3232, 11080, 37920, 129648, 443008, 1513248, 5168000, 17647552, 60258304, 205746304, 702484992, 2398480128, 8189016064, 27959235072, 95459170304, 325918735360, 1112757649408, 3799195224064
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OFFSET
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1,1
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COMMENTS
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a(n)=A181365(n,0).
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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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Table of n, a(n) for n=1..24.
Index entries for linear recurrences with constant coefficients, signature (6,-10,4).
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FORMULA
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G.f.=2z(1-z)^3/[(1-2z)(1-4z+2z^2)].
4*a(n) = 2*A007070(n)-2^n, n>1. - R. J. Mathar, Jul 22 2022
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EXAMPLE
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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.
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MAPLE
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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);
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MATHEMATICA
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CoefficientList[Series[(2x (1-x)^3)/((1-2x)(1-4x+2x^2)), {x, 0, 30}], x] (* Harvey P. Dale, Mar 29 2020 *)
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CROSSREFS
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Cf. A181365
Sequence in context: A262068 A148496 A217528 * A106434 A150228 A203038
Adjacent sequences: A181364 A181365 A181366 * A181368 A181369 A181370
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KEYWORD
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nonn,easy
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AUTHOR
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Emeric Deutsch, Oct 15 2010
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STATUS
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approved
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