A157424 Triangle read by rows, A157423 * (A052284 * 0^(n-k))

1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 1, 0, 0, 3, 0, 1, 0, 1, 0, 0, 5, 1, 0, 1, 0, 1, 0, 0, 7, 1, 1, 0, 1, 0, 3, 0, 0, 11, 1, 1, 1, 0, 2, 0, 5, 0, 0, 0, 17, 0, 1, 1, 1, 0, 3, 0, 7, 0, 0, 27, 1, 0, 1, 1, 2, 0, 5, 0, 11, 0, 0, 40

Offset

1,15

Comments

Row sums = A052284 starting at n=1: (1, 1, 1, 2, 3, 5, 7, 11, 17,...). As a property of eigentriangles, sum of n-th row terms = rightmost term of next row.

Links

Table of n, a(n) for n=1..79.

Formula

Triangle read by rows, A157423 * (A052284 * 0^(n-k)). A157423 = an infinite lower triangular matrix with A005171 in every column. (A052284 * 0^(n-k)) = an infinite lower triangular matrix with A052284: (1, 1, 1, 1, 2, 3, 5, 7, 11, 17, 27,...) as the main diagonal and the rest zeros.

Example

First few rows of the triangle =
1;
0, 1;
0, 0, 1;
1, 0, 0, 1;
0, 1, 0, 0, 2;
1, 0, 1, 0, 0, 3;
0, 1, 0, 1, 0, 0, 5;
1, 0, 1, 0, 2, 0, 0, 7;
1, 1, 0, 1, 0, 3, 0, 0, 11;
1, 1, 1, 0, 2, 0, 5,0, 0, 17;
0, 1, 1, 1, 0, 3, 0, 7, 0, 0, 27;
1, 0, 1, 1, 2, 0, 5, 0, 11, 0, 0, 40;
0, 1, 0, 1, 2, 3, 0, 7, 0, 17, 0, 0, 61;
1, 0, 1, 0, 2, 3, 5, 0, 11, 0, 27, 0, 0, 92;
...
Example: row 5 = (0, 1, 0, 0, 2) = termwise products of (0, 1, 0, 0, 1) and
(1, 1, 1, 1, 2); where (0, 1, 0, 0, 2) = row 5 of triangle A157423 and
(1, 1, 1, 1, 2) = the first 5 terms of A052284.

Crossrefs

Cf. A157423, A005171, A052284

Sequence in context: A216601 A283000 A145765 * A144961 A144627 A135929

Adjacent sequences: A157421 A157422 A157423 * A157425 A157426 A157427

Keyword

nonn,tabl

Author

Gary W. Adamson & Mats Granvik, Feb 28 2009

Status

approved