|
| |
|
|
A144172
|
|
Eigentriangle, row sums = A076739, the number of compositions into Fibonacci numbers.
|
|
1
| |
|
|
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
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
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.
|
|
|
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: A140531 A117316 A109189 * A166692 A046766 A003285
Adjacent sequences: A144169 A144170 A144171 * A144173 A144174 A144175
|
|
|
KEYWORD
| nonn,tabl
|
|
|
AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 12 2008
|
| |
|
|
