OFFSET
0,2
COMMENTS
LINKS
Alois P. Heinz, Rows n = 0..200, flattened
Marilena Barnabei, Flavio Bonetti, and Niccolò Castronuovo, Motzkin and Catalan Tunnel Polynomials, J. Int. Seq., Vol. 21 (2018), Article 18.8.8.
FORMULA
G.f. = G(t,z) = 1/(1 - 3z + z^2 - tz^2).
EXAMPLE
T(3,1)=6 because we have 010, 011, 012, 001, 101 and 201.
T(4,2)=1 because we have 0101.
Triangle starts:
1;
3;
8, 1;
21, 6;
55, 25, 1;
144, 90, 9;
MAPLE
G := 1/(1-3*z+z^2-t*z^2): Gser := simplify(series(G, z = 0, 15)): for n from 0 to 13 do P[n] := sort(coeff(Gser, z, n)) end do: for n from 0 to 13 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 31 2010
STATUS
approved