OFFSET
0,5
FORMULA
T(0,0)=1, T(n,k)=0 if k<0 or if k>n, T(n,k)=F(n-k+1)*T(n-1,k-1)+F(k+1)*T(n-1,k) where F(n)=Fibonacci(n)=A000045(n).
T(n,k)=Fibonacci[(n - k + 1)]*A(n - 1, k - 1) + Fibonacci[k ]*A(n - 1, k). - Roger L. Bagula, Sep 09 2008
EXAMPLE
Triangle begins:
1;
1, 1;
1, 2, 1;
1, 4, 4, 1;
1, 7, 16, 7, 1;
1, 12, 53, 53, 12, 1;
1, 20, 166, 318, 166, 20, 1;
1, 33, 492, 1784, 1784, 492, 33, 1;
1, 54, 1413, 9288, 17840, 9288, 1413, 54, 1;
1, 88, 3960, 46233, 163504, 163504, 46233, 3960, 88, 1;
1, 143, 10912, 221859, 1418549, 2616064, 1418549, 221859, 10912, 143, 1;
MATHEMATICA
T[n_, 1] := 1; T[n_, n_] := 1; T[n_, k_] := Fibonacci[(n - k + 1)]*T[ n - 1, k - 1] + Fibonacci[k ]*T[n - 1, k]; Table[Table[T[n, m], {m, 1, n}], {n, 1, 10}]; Flatten[%] - Roger L. Bagula, Sep 09 2008
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Feb 17 2007
STATUS
approved