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A181305 Number of increasing columns in all 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, 1, 5, 24, 104, 432, 1736, 6820, 26332, 100308, 377996, 1411844, 5234428, 19285252, 70670972, 257766212, 936336572, 3388962884, 12226547132, 43983439684, 157814634684, 564917186372, 2017873643708, 7193745818436 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also, number of odd entries in the top rows of all 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.

a(n)=Sum(A181304(n,k), k=0..n).

For the case of the even entries see A181337.

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.

Index entries for linear recurrences with constant coefficients, signature (7, -12, -4, 12, -4).

FORMULA

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

EXAMPLE

a(1)=1 because in the 2-compositions of 1, namely (0/1) and (1/0) we have only one increasing column (the 2-compositions are written as (top row / bottom row).

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 0+1+0+1+1+2+0=5 odd entries.

MAPLE

g := z*(1-z)^2/((1+z)*(1-4*z+2*z^2)^2): gser := series(g, z = 0, 30): seq(coeff(gser, z, k), k = 0 .. 27);

CROSSREFS

Cf. A181304, A181337.

Sequence in context: A078820 A291395 A179417 * A046724 A272578 A273622

Adjacent sequences:  A181302 A181303 A181304 * A181306 A181307 A181308

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Oct 13 2010

EXTENSIONS

Edited by N. J. A. Sloane, Oct 15 2010

STATUS

approved

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Last modified August 19 04:27 EDT 2019. Contains 326109 sequences. (Running on oeis4.)