A157424 - OEIS

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

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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 =

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