

A160756


Triangle read by rows, infinite lower triangular Toeplitz matrix with A078008 in every column convolved with A001333.


1



1, 0, 1, 2, 0, 1, 2, 2, 0, 3, 6, 2, 2, 0, 7, 10, 6, 2, 6, 0, 17, 22, 10, 6, 6, 14, 0, 41, 42, 22, 10, 18, 14, 34, 0, 99, 86, 42, 22, 30, 42, 34, 82, 0, 239, 170, 86, 42, 66, 70, 102, 82, 198, 0, 577
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OFFSET

0,4


COMMENTS

Row sums = A001333: (1, 1, 3, 7, 17, 41,...). Sum of nth row terms = rightmost term of next row.


LINKS

Table of n, a(n) for n=0..54.


FORMULA

Let M = an infinite lower triangular Toeplitz matrix with A078008 (1, 0, 2, 2, 6, 10, 22, 42, 86, 170,...). Let Q = the eigensequence of that triangle prefaced with a 1: (1, 1, 1, 3, 7, 17,...) where A001333 = (1, 1, 3, 7, 17,...). The triangle = M * Q.


EXAMPLE

First few rows of the triangle =
1;
0, 1;
2, 0, 1;
2, 2, 0, 3;
6, 2, 2, 0, 7;
10, 6, 2, 6, 0, 17;
22, 10, 6, 6, 14, 0, 41;
42, 22, 10, 18, 14, 34, 0, 99;
86, 42, 22, 30, 42, 34, 82, 0, 239;
170, 86, 42, 66, 70, 102, 82, 198, 0, 577;
...
Example: row 4 = (6, 2, 2, 0, 7) = (6, 2, 2, 0, 1) * (1, 1, 1, 3, 7).


CROSSREFS

Cf. A078008, A001333
Sequence in context: A113678 A299480 A110249 * A176239 A292475 A145462
Adjacent sequences: A160753 A160754 A160755 * A160757 A160758 A160759


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, May 25 2009


STATUS

approved



