|
| |
|
|
A194710
|
|
Triangle read by rows: T(k,m) = number of occurrences of k in the last section of the set of partitions of (10 + m).
|
|
9
|
|
|
|
42, 15, 27, 10, 14, 18, 5, 10, 10, 17, 4, 5, 8, 10, 15, 2, 5, 4, 8, 9, 14, 2, 2, 4, 5, 7, 9, 13, 1, 2, 2, 4, 4, 8, 8, 13, 1, 1, 2, 2, 4, 4, 7, 9, 12, 0, 1, 1, 2, 2, 4, 4, 7, 8, 13, 1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 12, 0, 1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 12
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Sub-triangle of A182703 and also of A194812. Note that the sum of row k is also the number of partitions of 10. For further information see A182703 and A135010.
|
|
|
LINKS
|
|
|
|
FORMULA
|
T(k,m) = A182703(10+m,k), with T(k,m) = 0 if k > 10+m.
Beginning with row k=11 each row starts with (k-11) 0's and ends with the subsequence 1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 12, the initial terms of A002865. - Alois P. Heinz, Feb 15 2012
|
|
|
EXAMPLE
|
Triangle begins:
42;
15, 27;
10, 14, 18;
5, 10, 10, 17;
4, 5, 8, 10, 15;
2, 5, 4, 8, 9, 14;
2, 2, 4, 5, 7, 9, 13;
1, 2, 2, 4, 4, 8, 8, 13;
1, 1, 2, 2, 4, 4, 7, 9, 12;
0, 1, 1, 2, 2, 4, 4, 7, 8, 13;
1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 12;
0, 1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 12;
0, 0, 1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 12;
0, 0, 0, 1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 12;
....
For k = 1 and m = 1; T(1,1) = 42 because there are 42 parts of size 1 in the last section of the set of partitions of 11, since 10 + m = 11, so a(1) = 42. For k = 2 and m = 1; T(2,1) = 15 because there are 15 parts of size 2 in the last section of the set of partitions of 11, since 10 + m = 11, so a(2) = 15.
|
|
|
CROSSREFS
|
Always the sum of row k = p(10) = A000041(10) = 42.
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
