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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
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.
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Oct 13 2010
STATUS
approved