

A179745


Triangle read by rows,derived from iterates of operations in which a current eigensequence becomes the left border of a new triangle; with triangles of the form: all 1's except the left border for triangles >1.


2



1, 1, 1, 1, 3, 1, 1, 7, 4, 1, 1, 15, 12, 5, 1, 1, 31, 32, 18, 6, 1, 1, 63, 80, 56, 25, 7, 1, 1, 1, 127, 192, 160, 88, 33, 8, 1, 1, 255, 448, 432, 280, 129, 42, 9, 1
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OFFSET

1,5


COMMENTS

Row sums of the triangle = odd indexed Fibonacci numbers, A001519(n).
Eigensequences of successive triangles tend to A001519: (1, 2, 5, 13, 34,...).


LINKS

Table of n, a(n) for n=1..46.


FORMULA

The triangle is derived from operations in two parts. First, form an array
in which rows = eigensequences of triangles of the form: (all 1's except the
left border). First triangle has all 1's. Eigensequence of this triangle =
(1, 2, 4, 8, 16, 32,...). We shift this to the right = (1, 1, 2, 4, 8, 16,...);
creating a new triangle with this sequence as the left border. Eigensequence
of this triangle = (1, 2, 5, 12, 28, 64,...). We shift this to the right,
making it the left border of the next triangle; and so on such that
eigensequence of current triangle becomes next triangle's left border.
.
The second operation takes finite differences of the array. Reorienting the
terms, we obtain triangle A179745.


EXAMPLE

First few rows of the array =
.
1,...2,...4,...8,....16,....32,...
1,...2,...5,..12,....28,....64,...
1,...2,...5,..13,....33,....82,...
1,...2,...5,..13,....34,....88,...
1,...2,...5,..13,....34,....89,...
.
Taking finite differences from the top, we reorient the terms obtaining
triangle A179745:
.
1;
1, 1;
1, 3, 1;
1, 7, 4, 1;
1, 15, 12, 5, 1;
1, 31, 32, 18, 6, 1;
1, 63, 80, 56, 25, 7, 1;
1, 127, 192, 160, 88, 33, 8, 1;
1, 255, 448, 432, 280, 129, 42, 9, 1;
...


CROSSREFS

Cf. A001519
Sequence in context: A078026 A126713 A140068 * A121300 A283595 A128119
Adjacent sequences: A179742 A179743 A179744 * A179746 A179747 A179748


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Jul 25 2010


STATUS

approved



