|
| |
|
|
A144152
|
|
Eigentriangle, row sums = Fibonacci numbers.
|
|
1
| |
|
|
1, 0, 1, 1, 0, 1, 0, 1, 0, 2, 1, 0, 1, 0, 3, 0, 1, 0, 2, 0, 5, 1, 0, 1, 0, 3, 0, 8, 0, 1, 0, 2, 0, 5, 0, 13, 1, 0, 1, 0, 3, 0, 8, 0, 21, 0, 1, 0, 2, 0, 0, 5, 0, 13, 0, 34, 1, 0, 1, 0, 3, 0, 8, 0, 21, 0, 55
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,10
|
|
|
COMMENTS
| Even n rows are composed of odd indexed Fibonacci numbers interpolated with zeros.
Odd n rows are composed of even indexed Fibonacci numbers with alternate zeros. Sum of n-th row terms = rightmost term of next row, = F(n-1). Row sums = F(n).
|
|
|
FORMULA
| Triangle read by rows, A128174 * X; X = an infinite lower triangular matrix with a shifted Fibonacci sequence: (1, 1, 1, 2, 3, 5, 8,...) in the main diagonal and the rest zeros. A128174 = the matrix: (1; 0,1; 1,0,1; 0,1,0,1;...). These operations are equivalent to termwise products of n terms of A128174 mattrix row terms and an equal number of terms in (1, 1, 1, 2, 3, 5, 8,...).
|
|
|
EXAMPLE
| First few rows of the triangle =
1;
0, 1;
1, 0, 1;
0, 1, 0, 2;
1, 0, 1, 0, 3
0, 1, 0, 2, 0, 5;
1, 0, 1, 0, 3, 0, 8;
0, 1, 0, 2, 0, 5, 0, 13;
1, 0, 1, 0, 3, 0, 8, 0, 21;
...
Row 5 = (1, 0, 1, 0, 3) = termwise products of (1, 0, 1, 0, 1) and (1, 1, 1, 2, 3).
|
|
|
CROSSREFS
| A000045, Cf. A128174
Sequence in context: A029406 A158461 A118269 * A116675 A123022 A072943
Adjacent sequences: A144149 A144150 A144151 * A144153 A144154 A144155
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 12 2008
|
| |
|
|
