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

1,6

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.

Links

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

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,...).

Example

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

Sequence in context: A109189 A264157 A361853 * A227318 A166692 A046766

Adjacent sequences: A144169 A144170 A144171 * A144173 A144174 A144175

Keyword

nonn,tabl

Author

Gary W. Adamson, Sep 12 2008

Status

approved