Revision History for A181290
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| A181290
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The sum of the lengths of the 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. The length of the 2-composition is the number of columns.
(history;
published version)
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#4 by R. J. Mathar at Fri Jul 22 12:30:49 EDT 2022
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#3 by R. J. Mathar at Fri Jul 22 12:30:46 EDT 2022
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| LINKS
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<a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-20,16,-4).
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| STATUS
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approved
editing
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#2 by Russ Cox at Fri Mar 30 17:36:24 EDT 2012
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| AUTHOR
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_Emeric Deutsch (deutsch(AT)duke.poly.edu), _, Oct 12 2010
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Discussion
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| Fri Mar 30
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| OEIS Server: https://oeis.org/edit/global/173
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#1 by N. J. A. Sloane at Wed Oct 20 03:00:00 EDT 2010
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| NAME
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The sum of the lengths of the 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. The length of the 2-composition is the number of columns.
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| DATA
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0, 2, 11, 52, 227, 944, 3800, 14944, 57748, 220128, 829968, 3101376, 11502704, 42393088, 155392768, 566918144, 2059768384, 7456496128, 26905720576, 96804463616, 347386161920, 1243665567744, 4442849839104, 15840448094208
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| OFFSET
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0,2
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| COMMENTS
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a(n)=Sum(k*A181289(n,k), 0<=k<=n).
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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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| FORMULA
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G.f.=z(2-z)(1-z)^2/(1-4z+2z^2)^2.
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| MAPLE
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g := z*(1-z)^2*(2-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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Cf. A181289
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| KEYWORD
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nonn,new
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| AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 12 2010
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| STATUS
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approved
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