OFFSET
0,3
COMMENTS
FORMULA
G.f. of column k is g[k]=G[k]-G[k-1], where G[0]:=1/(1-z-z^2), G[k]=1/(1-z-z^2-z^2*G[k-1]).
EXAMPLE
T(3,1)=3 because we have hUD, UhD and UDh.
Triangle starts:
1;
1;
2,1;
3,3;
5,10,1;
8,27,5;
13,72,23,1;
MAPLE
G[0]:=1/(1-z-z^2): for n to 13 do G[n]:=simplify(1/(1-z-z^2-z^2*G[n-1])) end do: g[0]:=G[0]: for n to 13 do g[n]:=simplify(G[n]-G[n-1]) end do: for n from 0 to 13 do gser[n]:=series(g[n], z=0, 40) end do: for n from 0 to 13 do seq(coeff(gser[k], z, n), k=0..floor((1/2)*n)) end do;
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Sep 05 2007
STATUS
approved