

A181326


Number of columns with an odd sum 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.


2



0, 2, 8, 40, 168, 696, 2776, 10864, 41800, 158816, 597176, 2226512, 8242344, 30328160, 111013784, 404518640, 1468154504, 5309771264, 19143323000, 68823556368, 246805713000, 883028659744, 3152718627672, 11234773009200
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OFFSET

0,2


COMMENTS

a(n)=Sum(A181308(n,k), k=0..n).
For the "even sum" case, see A181328.


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 (6,5,16,8,8,4).


FORMULA

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


EXAMPLE

a(2)=8 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+0+0+2+2+2+2=8 columns with odd sums.


MAPLE

g := 2*z*(1z)^2/((1+z)^2*(14*z+2*z^2)^2): gser := series(g, z = 0, 30): seq(coeff(gser, z, n), n = 0 .. 27);


CROSSREFS

Cf. A181308, A181327, A181328
Sequence in context: A127919 A074092 A003445 * A220964 A231125 A221587
Adjacent sequences: A181323 A181324 A181325 * A181327 A181328 A181329


KEYWORD

nonn,easy


AUTHOR

Emeric Deutsch, Oct 13 2010


STATUS

approved



