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A181326 Number of columns with an odd sum 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. 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 (list; graph; refs; listen; history; text; internal format)
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 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 (6,-5,-16,8,8,-4).

FORMULA

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

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Last modified February 4 14:43 EST 2023. Contains 360055 sequences. (Running on oeis4.)