A144219 Eigentriangle, row sums = number of ordered partitions of n into powers of 2

1, 1, 1, 0, 1, 2, 1, 0, 2, 3, 0, 1, 0, 3, 6, 0, 0, 2, 0, 6, 10, 0, 0, 0, 3, 0, 10, 18, 1, 0, 0, 0, 6, 0, 18, 31, 0, 1, 0, 0, 0, 10, 0, 31, 56, 0, 0, 2, 0, 0, 0, 18, 0, 56, 98, 0, 0, 0, 3, 0, 0, 0, 31, 0, 98, 174, 0, 0, 0, 0, 6, 0, 0, 0, 56, 0, 174, 306, 0, 0, 0, 0, 0, 10, 0, 0, 98, 0, 306, 542, 0, 0

Offset

1,6

Comments

Right border of the triangle = A023359: (1, 1, 2, 3, 6, 10, 18,...) the number of ordered partitions of n into powers of 2.

Row sums = A023359 starting with offset 1: (1, 2, 3, 6, 10, 18,...).

Sum of n-th row terms = rightmost term of next row.

Links

Table of n, a(n) for n=1..92.

Formula

Equals A*B, where A = an infinite lower triangular matrix with the Fredholm-Rueppel sequence A036987 in every column: (1, 1, 0, 1, 0, 0, 0, 1,...); and B = an infinite lower triangular matrix with A023359: (1, 1, 2, 3, 6, 10, 18,...) as the main diagonal and the rest zeros.

Example

First few rows of the triangle =
1;
1, 1;
0, 1, 2;
1, 0, 2, 3;
0, 1, 0, 3, 6;
0, 0, 2, 0, 6, 10;
0, 0, 0, 3, 0, 10, 18;
1, 0, 0, 0, 6, 0, 18, 31;
0, 1, 0, 0, 0, 10, 0, 31, 56;
0, 0, 2, 0, 0, 0, 18, 0, 56; 98;
0, 0, 0, 3, 0, 0, 0, 31, 0, 98, 174;
0, 0, 0, 0, 6, 0, 0, 0, 56, 0, 174, 306;
...
Row 4 = (1, 0, 2, 3) = termwise products of (1, 0, 1, 1) and (1, 1, 2, 3).

Crossrefs

Sequence in context: A097854 A161515 A145580 * A144027 A019591 A353984

Adjacent sequences: A144216 A144217 A144218 * A144220 A144221 A144222

Keyword

nonn,tabl

Author

Gary W. Adamson, Sep 14 2008

Status

approved