A144172 Eigentriangle, row sums = A076739, the number of compositions into Fibonacci numbers.

1, 1, 1, 1, 1, 2, 0, 1, 2, 4, 1, 0, 2, 4, 7, 0, 1, 0, 4, 7, 14, 0, 0, 2, 0, 7, 14, 26, 1, 0, 0, 4, 0, 14, 26, 49, 0, 1, 0, 0, 7, 0, 26, 49, 94, 0, 0, 2, 0, 0, 14, 0, 49, 94, 177, 0, 0, 0, 4, 0, 0, 26, 0, 94, 177, 336, 0, 0, 0, 0, 7, 0, 0, 49, 0, 177, 336, 637

Offset: 1

Author

Gary W. Adamson, Sep 12 2008

Keywords

• nonn
• tabl

Comments

Row sums = A076739 starting with offset 1: (1, 2, 4, 7, 14, 26, 49,...).

Left border = A010056, the characteristic function of the Fibonacci numbers Starting with offset 1: (1, 1, 1, 0, 1,...).

Sum of n-th row terms = rightmost term of next row.

Right border = A076739.

Examples

			First few rows of the triangle =
1;
1, 1;
1, 1, 2;
0, 1, 2, 4;
1, 0, 2, 4, 7;
0, 1, 0, 4, 7, 14;
0, 0, 2, 0, 7, 14, 26;
1, 0, 0, 4, 0, 14, 26, 49;
0, 1, 0, 0, 7, 0, 26, 49, 94;
0, 0, 2, 0, 0, 14, 0, 49, 94, 177;
0, 0, 0, 4, 0, 0, 26, 0, 94, 177, 336;
0, 0, 0, 0, 7, 0, 0, 49, 0, 177, 336, 637;
1, 0, 0, 0, 0, 14, 0, 0, 94, 0, 336, 637, 1206;
...
Example: row 5 = (1, 0, 2, 4, 7) = termwise product of (1, 0, 1, 1, 1) and (1, 1, 2, 4, 7).
		

Crossrefs

A076739, Cf. A010056

Formula

T(n,k) = A010056(n-k+1)*A076739(k-1). A010056, the characteristic function of the Fibonacci numbers, starts with offset 1: (1, 1, 1, 0, 1,...). A076739(k-1), the INVERTi transform of (1, 1, 1, 0, 1,...) starts with offset 0: (1, 1, 2, 4, 7, 14,...).