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A144219 Eigentriangle, row sums = number of ordered partitions of n into powers of 2 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 (list; table; graph; refs; listen; history; text; internal format)
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

Let 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.

Triangle A144219 = A*B. triangle

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, 0, 2, 3).

CROSSREFS

Sequence in context: A097854 A161515 A145580 * A144027 A019591 A091967

Adjacent sequences:  A144216 A144217 A144218 * A144220 A144221 A144222

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Sep 14 2008

STATUS

approved

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Last modified October 22 23:18 EDT 2018. Contains 316518 sequences. (Running on oeis4.)