cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-1 of 1 results.

A234713 Triangle, read by rows, based on the Fibonacci numbers.

Original entry on oeis.org

0, 1, 1, 1, 3, 2, 2, 6, 7, 3, 3, 13, 20, 14, 4, 5, 25, 51, 51, 25, 5, 8, 48, 118, 154, 111, 41, 6, 13, 89, 260, 416, 393, 217, 63, 7, 21, 163, 548, 1042, 1218, 890, 392, 92, 8, 34, 294, 1121, 2465, 3435, 3127, 1842, 666, 129, 9, 55, 525, 2236, 5586, 9035, 9845
Offset: 0

Views

Author

Philippe Deléham, Dec 29 2013

Keywords

Comments

First column is the Fibonacci sequence.
Sum_{k=0..n} T(n,k)*2^k = -A106732(n).

Examples

			Triangle begins:
0
1, 1
1, 3, 2
2, 6, 7, 3
3, 13, 20, 14, 4
5, 25, 51, 51, 25, 5
8, 48, 118, 154, 111, 41, 6
13, 89, 260, 416, 393, 217, 63, 7
21, 163, 548, 1042, 1218, 890, 392, 92, 8
		

Crossrefs

Cf. Diagonals: A001477, A004006.
Cf. Columns: A000045 (Fibonacci), A131913, A261054.
Cf. A025192 (row sums for n>0), A006054 (diagonal sums)

Formula

G.f.: (y+1)*x/(1-(2y+1)*x+(y^2-1)*x^2).
T(n,k)=T(n-1,k)+2*T(n-1,k-1)+T(n-2,k)-T(n-2,k-2), T(0,0)=0, T(1,0)=1, T(1,1)=1, T(n,k)=0 if k<0 or if k>n.
Showing 1-1 of 1 results.