OFFSET
0,2
COMMENTS
FORMULA
G.f. = G(t,z) = (1+tz)/(1-2z-z^2-2tz^2).
T(n,k) = 2T(n-1,k) + T(n-2,k) + 2T(n-2,k-1) (n >= 2).
EXAMPLE
T(4,2)=12 because we have 0101, 0102, 0110, 0120, 0201, 0202, 0210, 0220, 1010, 1020, 2010 and 2020.
Triangle starts:
1;
2, 1;
5, 4;
12, 13, 2;
29, 40, 12;
70, 117, 52, 4;
MAPLE
G:=(1+t*z)/(1-2*z-z^2-2*t*z^2): Gser:=simplify(series(G, z=0, 14)): P[0]:=1: for n from 1 to 12 do P[n]:=sort(coeff(Gser, z^n)) od: for n from 0 to 12 do seq(coeff(P[n], t, j), j=0..ceil(n/2)) od; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, May 29 2006
STATUS
approved