OFFSET
0,2
COMMENTS
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. = G(t,z)=(1-z)^2/(1-4z+3z^2-tz^2).
The g.f. of column k is z^{2k}/[(1-3z)^{k+1}*(1-z)^{k-1}] (we have a Riordan array).
EXAMPLE
T(2,1)=1 because we have (1/1) (the 2-compositions are written as (top row / bottom row).
Triangle starts:
1;
2;
6,1;
18,6;
54,27,1;
162,108,10;
MAPLE
G := (1-z)^2/(1-4*z+3*z^2-t*z^2): Gser := simplify(series(G, z = 0, 15)): for n from 0 to 12 do P[n] := sort(coeff(Gser, z, n)) end do: for n from 0 to 12 do seq(coeff(P[n], t, k), k = 0 .. floor((1/2)*n)) end do; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Oct 13 2010
STATUS
approved