OFFSET
0,3
COMMENTS
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.
LINKS
G. Castiglione, A. Frosini, E. Munarini, A. Restivo and S. Rinaldi, Combinatorial aspects of L-convex polyominoes, European J. Combin. 28 (2007), no. 6, 1724-1741.
Index entries for linear recurrences with constant coefficients, signature (8,-20,16,-4).
FORMULA
EXAMPLE
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 2-compositions are written as (top row / bottom row)) we have 1+0+1+1+1+0+2=5 zeros.
MAPLE
g := z*(1-z)^3/(1-4*z+2*z^2)^2: gser := series(g, z = 0, 30): seq(coeff(gser, z, n), n = 0 .. 27);
MATHEMATICA
LinearRecurrence[{8, -20, 16, -4}, {0, 1, 5, 23, 99}, 25] (* Georg Fischer, Feb 01 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Oct 13 2010
STATUS
approved