A160756 Triangle read by rows, infinite lower triangular Toeplitz matrix with A078008 in every column convolved with A001333.

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

Offset

0,4

Comments

Row sums = A001333: (1, 1, 3, 7, 17, 41,...). Sum of n-th 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: A328708 A299480 A110249 * A306327 A176239 A361854

Adjacent sequences: A160753 A160754 A160755 * A160757 A160758 A160759

Keyword

nonn,tabl

Author

Gary W. Adamson, May 25 2009

Status

approved