OFFSET
0,2
COMMENTS
LINKS
Alois P. Heinz, Rows n = 0..150, flattened
FORMULA
G.f.: G(t,z)=[1+(1-t)z+(1-t)z^2]/[1-(2+t)z-2(1-t)z^2-2(1-t)z^3].
EXAMPLE
T(5,2) = 4 because we have 00001, 00002, 10000 and 20000.
Triangle starts:
1;
3;
9;
26, 1;
76, 4, 1;
222, 16, 4, 1;
...
MAPLE
G:=(1+(1-t)*z+(1-t)*z^2)/(1-(2+t)*z-2*(1-t)*z^2-2*(1-t)*z^3): Gser:=simplify(series(G, z=0, 15)): P[0]:=1: for n from 1 to 12 do P[n]:=sort(coeff(Gser, z^n)) od: 1; 3; for n from 2 to 12 do seq(coeff(P[n], t, j), j=0..n-2) od; # yields sequence in triangular form
MATHEMATICA
nn=10; f[list_]:=Select[list, #>0&]; a=x^2/(1-y x) +x; Map[f, CoefficientList[Series[(a+1)/(1-2x-2x a), {x, 0, nn}], {x, y}]]//Grid (* Geoffrey Critzer, Oct 31 2012 *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, May 26 2006
STATUS
approved