

A140068


Triangle read by rows, nth row = (n1)th power of the matrix X * [1,0,0,0,...] where X = an infinite lower triangular matrix with [1,2,1,2,1,2,...] in the main diagonal and [1,1,1,...] in the subdiagonal.


2



1, 1, 1, 1, 3, 1, 1, 7, 4, 1, 1, 15, 11, 6, 1, 1, 31, 26, 23, 7, 1, 1, 63, 57, 72, 30, 9, 1, 1, 127, 120, 201, 102, 48, 10, 1, 1, 255, 247, 522, 303, 198, 58, 12, 1, 1, 511, 502, 1291, 825, 699, 256, 82, 13, 1, 1, 1023, 1013, 3084, 2116, 2223, 955, 420, 95, 15, 1, 1, 2047, 2036
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OFFSET

1,5


COMMENTS

Sum of nth row terms = odd indexed Fibonacci numbers, F(2n+1); e.g. sum of row 5 terms = (1 + 15 + 11 + 6 + 1) = 34 = F(9).
The triangle is a companion to A140069 (having row sums = even indexed Fibonacci numbers).


LINKS

Table of n, a(n) for n=1..69.


FORMULA

Triangle read by rows, nth row = (n1)th power of the matrix X * [1,0,0,0,...] where X = an infinite lower triangular matrix with [1,2,1,2,1,2,...] in the main diagonal and [1,1,1,...] in the subdiagonal. Given the matrix X, perform X * [1,0,0,0,...] and then iterate: X * (result), etc. and record the result as each successive row of the triangle.


EXAMPLE

First few rows of the triangle are:
1;
1, 1;
1, 3, 1;
1, 7, 4, 1;
1, 15, 11, 6, 1;
1, 31, 26, 23, 7, 1;
1, 63, 57, 72, 30, 9, 1;
1, 127, 120, 201, 102, 48, 10, 1;
1, 255, 247, 522, 303, 198, 58, 12, 1;
...


CROSSREFS

Cf. A140069.
Sequence in context: A135288 A078026 A126713 * A179745 A121300 A283595
Adjacent sequences: A140065 A140066 A140067 * A140069 A140070 A140071


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson and Roger L. Bagula, May 04 2008


STATUS

approved



