

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
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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 nth row terms = rightmost term of next row, = F(n1). Row sums = F(n).


LINKS

Table of n, a(n) for n=1..67.


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 matrix 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: A158461 A281498 A118269 * A265674 A229297 A116675
Adjacent sequences: A144149 A144150 A144151 * A144153 A144154 A144155


KEYWORD

nonn


AUTHOR

Gary W. Adamson, Sep 12 2008


STATUS

approved



