|
|
A125104
|
|
Triangle read by rows counting compositions (ordered partitions) by minimal part size.
|
|
1
|
|
|
1, 1, 1, 1, 0, 3, 1, 0, 1, 6, 1, 0, 0, 2, 13, 1, 0, 0, 1, 3, 27, 1, 0, 0, 0, 2, 5, 56, 1, 0, 0, 0, 1, 2, 9, 115, 1, 0, 0, 0, 0, 2, 3, 15, 235, 1, 0, 0, 0, 0, 1, 2, 5, 25, 478, 1, 0, 0, 0, 0, 0, 2, 2, 8, 42, 969, 1, 0, 0, 0, 0, 0, 1, 2, 3, 12, 70, 1959, 1, 0, 0, 0, 0, 0, 0, 2, 2, 5, 18, 116, 3952, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 8, 27, 192, 7959, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 3, 11, 41, 317, 16007
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,6
|
|
COMMENTS
|
The diagonals of this array can be generated from Table A099238 as follows: A000079 - A000045 = [1, 2, 4, 8, 16, 32, ...] - [0, 1, 1, 2, 3, 5, ...] = [1, 1, 3, 6, 13, 27, ...] = A099036, A000045 - A000930, A000930 - A003269, A003269 - A003520, etc.
|
|
LINKS
|
|
|
EXAMPLE
|
Row 4 of the array is (1, 0, 1, 6) because there are six compositions with minimum part of size one: 1111, 31, 13, 211, 121, 112; one of size two: 22; none of size three; and 1 of size four: 4.
Triangle (after 45-degree counterclockwise rotation) begins:
1 1 3 6 13 27 56 115 235 478 969 1959 3952 7959
.1 0 1 2 3 5 9 15 25 42 70 116 192
..1 0 0 1 2 2 3 5 8 12 18 27
...1 0 0 0 1 2 2 2 3 5 8
....1 0 0 0 0 1 2 2 2 2
.....1 0 0 0 0 0 1 2 2
......1 0 0 0 0 0 0 1
.......1 0 0 0 0 0 0
........1 0 0 0 0 0
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|