A139147 Triangle read by rows: replace A003983(n,k) with F(n).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 3, 2, 1, 1, 1, 1, 2, 3, 3, 2, 1, 1, 1, 1, 2, 3, 5, 3, 2, 1, 1, 1, 1, 2, 3, 5, 5, 3, 2, 1, 1, 1, 1, 2, 3, 5, 8, 5, 3, 2, 1, 1, 1, 1, 2, 3, 5, 8, 8, 5, 3, 2, 1, 1

Offset: 1

Author

Gary W. Adamson & Klaus Breyer, Apr 10 2008

Keywords

• nonn
• tabl

Examples

			First few rows of A003983 are [1; 1,1; 1,2,1; 1,2,2,1;...] which become [F(1); F(1),F(1); F(1),F(2),F(1); F(1),F(2),F(2),F(1);...] =
1;
1, 1;
1, 1, 1;
1, 1, 1, 1;
1, 1, 2, 1, 1;
1, 1, 2, 2, 1, 1;
1, 1, 2, 3, 2, 1, 1;
1, 1, 2, 3, 3, 2, 1, 1;
1, 1, 2, 3, 5, 3, 2, 1, 1;
1, 1, 2, 3, 5, 5, 3, 2, 1, 1;
1, 1, 2, 3, 5, 8, 5, 3, 2, 1, 1;
...
		

Crossrefs

Cf. A134404.

Formula

Replace term A003983(n,k) with F(n).

Triangle T(n,k)=sum{j=0..n, [j<=k]*[j<=n-k]*(F(j+1)-F(j))}. [From Paul Barry, Jan 18 2009]