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