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A181298 The number of even entries in all 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. 3
0, 2, 12, 56, 246, 1024, 4128, 16248, 62832, 239640, 903944, 3379064, 12536552, 46215672, 169443592, 618303864, 2246863624, 8135066488, 29358346888, 105642047864, 379143054472, 1357496762744, 4849952390792, 17293404551544 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n)=Sum(k*A181297(n,k),k=0..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.

LINKS

Table of n, a(n) for n=0..23.

FORMULA

G.f. = 2z(1-z)^2*(1+z-z^2)/[(1+z)(1-4z+2z^2)^2].

EXAMPLE

a(2)=12 because in the 2-compositions of 2, namely (1/1),(0/2),(2/0),(1,0/0,1),(0,1/1,0),(1,1/0,0), and (0,0/1,1), we have 0+2+2+2+2+2+2=12 odd entries (the 2-compositions are written as (top row/bottom row)).

MAPLE

g := 2*z*(1-z)^2*(1+z-z^2)/((1+z)*(1-4*z+2*z^2)^2): gser := series(g, z = 0, 30): seq(coeff(gser, z, n), n = 0 .. 25);

CROSSREFS

Cf. A181295, A181296, A181297.

Sequence in context: A127221 A020522 A037130 * A247121 A078543 A084128

Adjacent sequences:  A181295 A181296 A181297 * A181299 A181300 A181301

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Oct 12 2010

STATUS

approved

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Last modified August 24 13:48 EDT 2019. Contains 326279 sequences. (Running on oeis4.)