

A152251


Eigentriangle, row sums = A001519, oddindexed Fibonacci numbers.


2



1, 1, 1, 2, 1, 2, 4, 2, 2, 5, 8, 4, 4, 5, 13, 16, 8, 8, 10, 13, 34, 32, 16, 16, 20, 26, 34, 89, 64, 32, 32, 40, 52, 68, 89, 233, 128, 64, 64, 80, 104, 136, 178, 233, 610
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OFFSET

1,4


COMMENTS

Row sums = A001519, the odd indexed Fibonacci numbers starting (1, 2, 5, 13, 34,...).
Sum of nth row terms = rightmost term of next row.


LINKS

Table of n, a(n) for n=1..45.


FORMULA

Triangle read by rows, M*Q. M = an infinite lower triangular matrix with (1, 1, 2, 4, 8, 16,...) in every column and Q = a matrix (1, 1, 2, 5, 13, 34,...) as the main diagonal and the rest zeros.
Let M = production matrix for reversed rows of the triangle as follows:
1, 1;
1, 0, 2;
1, 0, 0, 2;
1, 0, 0, 0, 2;
1, 0, 0, 0, 0, 2;
...
Reversal of nth row of triangle A152251 = top row terms of M^(n1). Example: top row of M^3 = (5, 2, 2, 4).  Gary W. Adamson, Jul 07 2011


EXAMPLE

First few rows of the triangle =
1;
1, 1;
2, 1, 2;
4, 2, 2, 5;
8, 4, 4, 5, 13;
16, 8, 8, 10, 13, 34;
32, 16, 16, 20, 26, 34, 89;
64, 32, 32, 40, 52, 68, 89, 233;
128, 64, 64, 80, 104, 136, 178, 233, 610;
...
Row 4 = (8, 4, 4, 5, 13) = termwise products of (8, 4, 2, 1, 1) and (1, 1, 2, 5, 13).


CROSSREFS

Cf. A001519.
Sequence in context: A082793 A114929 A247321 * A144025 A058573 A184990
Adjacent sequences: A152248 A152249 A152250 * A152252 A152253 A152254


KEYWORD

eigen,nonn,tabl


AUTHOR

Gary W. Adamson, Nov 30 2008


EXTENSIONS

Last term corrected by Olivier Gérard, Aug 11 2016


STATUS

approved



