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

1,13

Links

Table of n, a(n) for n=1..78.

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]

Example

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.

Sequence in context: A274193 A238384 A139040 * A055801 A155050 A140356

Adjacent sequences: A139144 A139145 A139146 * A139148 A139149 A139150

Keyword

nonn,tabl

Author

Gary W. Adamson & Klaus Breyer, Apr 10 2008

Status

approved