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A140069 Triangle read by rows, n-th row = (n-1)-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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Sum of n-th 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, n-th row = (n-1)-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

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Last modified October 19 03:22 EDT 2018. Contains 316327 sequences. (Running on oeis4.)