

A145007


Eigentriangle of the partition numbers.


2



1, 1, 0, 1, 1, 0, 0, 1, 2, 0, 0, 0, 2, 3, 0, 1, 0, 0, 3, 5, 0, 1, 0, 0, 1, 0, 0, 5, 7, 0, 1, 0, 2, 0, 0, 7, 11, 0, 0, 1, 0, 3, 0, 0, 11, 15, 0, 0, 0, 2, 0, 5, 0, 0, 15, 22, 0, 0, 0, 0, 3, 0, 7, 0, 0, 22, 30, 0, 0, 0, 0, 0, 5, 0, 11, 0, 0, 30, 42, 0, 1, 0, 0, 0, 0, 7, 0, 15, 0, 0, 42, 56
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,9


COMMENTS

Sum of nth row terms = rightmost nonzero term of next row.
Row sums = the partition numbers, A000041, as well as the rightmost diagonal with no zeros.


LINKS

Table of n, a(n) for n=0..91.


FORMULA

Triangle read by rows, termwise products of A000041 (the partition numbers); and the partition number generator, A145006.


EXAMPLE

First few rows of the triangle =
1;
1, 0;
1, 1, 0;
0, 1, 2, 0;
0, 0, 2, 3, 0;
1, 0, 0, 3, 5, 0;
0, 1, 0, 0, 5, 7, 0;
1, 0, 2, 0, 0, 7, 11, 0,;
0, 1, 0, 3, 0, 0, 11, 15, 0;
0, 0, 2, 0, 5, 0, 0, 15, 22, 0;
0, 0, 0, 3, 0, 7, 0, 0, 22, 30, 0;
0, 0, 0, 0, 5, 0, 11, 0, 0, 30, 42, 0;
1, 0, 0, 0, 0, 7, 0, 15, 0, 0, 42, 56, 0;
0, 1, 0, 0, 0, 0, 11, 0, 22, 0, 0, 56, 77, 0;
0, 0, 2, 0, 0, 0, 0, 15, 0, 30, 0, 0, 77, 101, 0;
...
Example: row 4 = (0, 0, 2, 3) = termwise products of (0, 0, 1, 1) and (1, 1, 2, 3), where (0, 0, 1, 1) = row 4 of triangle A145006. The partition numbers = (1, 1, 2, 3, 5, 7, 11, 15,...).


CROSSREFS

Sequence in context: A057108 A063958 A126164 * A228616 A151670 A153587
Adjacent sequences: A145004 A145005 A145006 * A145008 A145009 A145010


KEYWORD

eigen,tabl,sign


AUTHOR

Gary W. Adamson, Sep 28 2008


STATUS

approved



