OFFSET
0,2
COMMENTS
FORMULA
T(n,k)=F(n-2k+1) if 2k+1<n, where F(j) are the Fibonacci numbers (F(0)=0, F(1)=1); T(2k+1,k)=2; T(n,k)=0 if 2k>n. G.f.=G(t,z)=(1+z)(1-z^2)/[(1-z-z^2)(1-tz^2)].
EXAMPLE
T(7,2)=3 because we have 0101110, 0101111 and 0101101.
Triangle starts:
1;
2;
2,1;
3,2;
5,2,1;
8,3,2;
13,5,2,1;
MAPLE
with(combinat): T:=proc(n, k) if n=2*k+1 then 2 elif n<2*k then 0 else fibonacci(n-2*k+1) fi end: for n from 0 to 18 do seq(T(n, k), k=0..floor(n/2)) od; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, May 12 2007
STATUS
approved