OFFSET
0,5
COMMENTS
FORMULA
G.f. G=G(t,z) satisfies z*G^2 - (1 - z^3 + tz^3)*G + 1 - z^2 + tz^2 = 0.
EXAMPLE
T(2,1)=1 because we have \/ .
Triangle starts:
1;
1;
1, 1;
4, 1;
11, 3;
32, 10;
98, 33, 1;
MAPLE
eq := z*G^2-(1-z^3+t*z^3)*G+1-z^2+t*z^2: G := RootOf(eq, G): Gser := simplify(series(G, z = 0, 18)): for n from 0 to 15 do P[n] := sort(coeff(Gser, z, n)) end do: 1; 1; 1, 1; for n from 3 to 15 do seq(coeff(P[n], t, j), j = 0 .. floor((1/3)*n)) end do; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, May 31 2010
STATUS
approved