login
A181328
Number of columns with an even 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, 0, 3, 12, 59, 248, 1024, 4080, 15948, 61312, 232792, 874864, 3260360, 12064928, 44378984, 162399504, 591613880, 2146724864, 7762397576, 27980907248, 100580448920, 360636908000, 1290131211432, 4605675085008, 16410645183928
OFFSET
0,3
COMMENTS
a(n)=Sum(A181327(n,k), k>=0).
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. = z^2*(1-z)^2*(3-z^2)/[(1+z)(1-4z+2z^2)]^2.
a(n) = (3*A181326(n-1) -A181326(n-3))/2. - R. J. Mathar, Jul 24 2022
EXAMPLE
a(2)=3 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 1+1+1+0+0+0+0=3 columns with even sums.
MAPLE
g := z^2*(1-z)^2*(3-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
AUTHOR
Emeric Deutsch, Oct 13 2010
STATUS
approved