OFFSET
0,5
COMMENTS
FORMULA
G.f. = G(t,z) = (1+z)(1-z+tz)/(1-z-tz^2).
T(n,k) = binomial(n-k,k-1) + 2*binomial(n-k-1,k-1) + binomial(n-k-2,k-1) for n >= 4 and 0 <= k < floor((n+1)/2).
EXAMPLE
T(6,3)=5 because we have 110101, 101101, 101010, 101011 and 010101.
Triangle starts:
1;
1, 1;
0, 3;
0, 4, 1;
0, 4, 4;
0, 4, 8, 1;
0, 4, 12, 5;
MAPLE
G:=(1+z)*(1-z+t*z)/(1-z-t*z^2): Gser:=simplify(series(G, z=0, 21)): for n from 0 to 18 do P[n]:=sort(coeff(Gser, z, n)) od: for n from 0 to 17 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 12 2007
STATUS
approved