

A140069


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


3



1, 2, 1, 4, 3, 1, 8, 7, 5, 1, 16, 15, 17, 6, 1, 32, 31, 49, 23, 8, 1, 64, 63, 129, 72, 39, 9, 1, 128, 127, 321, 201, 150, 48, 11, 1, 256, 255, 769, 522, 501, 198, 70, 12, 1, 512, 511, 1793, 1291, 1524, 699, 338, 82, 14, 1, 1024, 1023, 4097, 3084, 4339, 2223, 1375, 420
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OFFSET

1,2


COMMENTS

Sum of nth row terms = A001906(2n). Example: sum of 4th row terms = ( 8 + 7 + 5 + 1) = 21 = A001906(8).


LINKS

Table of n, a(n) for n=1..63.


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, with rest zeros. Perform X * [1,0,0,0,...], X * result, etc; with the result of each operation generating successive rows of the triangle.
Binomial transform of A135225, as lower triangular matrices: a(n+1,k+1) = sum_{j=0..n} binomial(n,j)*A135225(j,k).  Gary W. Adamson, Mar 01 2012


EXAMPLE

First few rows of the triangle are:
1;
2, 1;
4, 3, 1;
8, 7, 5, 1;
16, 15, 17, 6, 1;
32, 31, 49, 23, 8, 1;
64, 63, 129, 72, 39, 9, 1;
128, 127, 321, 201, 150, 48, 11, 1;
256, 255, 769, 522, 501, 198, 70, 12, 1;
512, 511, 1793, 1291, 1524, 699, 338, 82, 14, 1;
1024, 1023, 4097, 3084, 4339, 2223, 1375, 420, 110, 15, 1;
...


CROSSREFS

Cf. A140068.
Cf. A135225.
Sequence in context: A276562 A055248 A103316 * A105851 A106195 A247023
Adjacent sequences: A140066 A140067 A140068 * A140070 A140071 A140072


KEYWORD

nonn,tabl


AUTHOR

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


STATUS

approved



