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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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified January 17 18:48 EST 2019. Contains 319251 sequences. (Running on oeis4.)