OFFSET
0,2
COMMENTS
LINKS
Alois P. Heinz, Rows n = 0..250, flattened
FORMULA
G.f.: G(t,z) = 1/[1-2z+(1-t)z^3]. Recurrence relation: T(n,k) = 2T(n-1,k) -T(n-3,k) +T(n-3,k-1) for n>=3.
EXAMPLE
T(7,2) = 6 because we have 0bb, 1bb, b0b, b1b, bb0 and bb1, where b=001.
Triangle starts:
1;
2;
4;
7, 1;
12, 4;
20, 12;
33, 30, 1;
MAPLE
G:=1/(1-2*z+(1-t)*z^3): Gser:=simplify(series(G, z=0, 20)): P[0]:=1: for n from 1 to 17 do P[n]:=coeff(Gser, z^n) od: for n from 0 to 17 do seq(coeff(P[n], t, j), j=0..floor(n/3)) od; # yields sequence in triangular form
MATHEMATICA
nn=15; Map[Select[#, #>0&]&, CoefficientList[Series[1/(1-2z-(u-1)z^3), {z, 0, nn}], {z, u}]]//Grid (* Geoffrey Critzer, Dec 03 2013 *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Apr 27 2006
STATUS
approved