

A181305


Number of increasing columns in all 2compositions of n. A 2composition 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
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OFFSET

0,3


COMMENTS

Also, number of odd entries in the top rows of all 2compositions of n. A 2composition 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 Lconvex polyominoes, European Journal of Combinatorics, 28, 2007, 17241741.


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(1z)^2/[(1+z)(14z+2z^2)^2].


EXAMPLE

a(1)=1 because in the 2compositions of 1, namely (0/1) and (1/0) we have only one increasing column (the 2compositions 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 2compositions are written as (top row/bottom row)) we have 0+1+0+1+1+2+0=5 odd entries.


MAPLE

g := z*(1z)^2/((1+z)*(14*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



