OFFSET
1,4
COMMENTS
The compressed form seems easier to understand. This is A322762 but with each partition, after it has been transformed, written as the string of its parts.
REFERENCES
D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.2.1.5, Problem 73, pp. 415, 761.
LINKS
Alois P. Heinz, Rows n = 1..24, flattened
EXAMPLE
In compressed form (see A322762) triangle begins:
1,
1, 12,
1, 11, 123,
1, 11, 12, 112, 1234,
1, 11, 11, 112, 121, 1123, 12345,
1, 11, 11, 112, 12, 111, 1123, 123, 1212, 11234, 123456,
...
For example, the 11 partitions of 6 are:
6, 51, 42, 411, 33, 321, 3111, 222, 2211, 21111, 111111,
and applying the transformation we get:
1, 11, 11, 112, 12, 111, 1123, 123, 1212, 11234, 123456.
In the uncompressed notation the triangle begins:
{1},
{1}, {1,2},
{1}, {1,1}, {1,2,3},
{1}, {1,1}, {1,2}, {1,1,2}, {1,2,3,4},
{1}, {1,1}, {1,1}, {1,1,2}, {1,2,1}, {1,1,2,3}, {1,2,3,4,5},
...
MAPLE
b:= (n, i)-> `if`(n=0 or i=1, [[$1..n]], [(t->
seq(map(x-> [$1..(t+1-j), x[]], b(n-i*(t+1-j)
, i-1))[], j=1..t))(iquo(n, i)), b(n, i-1)[]]):
T:= n-> map(x-> x[], b(n$2))[]:
seq(T(n), n=1..10); # Alois P. Heinz, Dec 30 2018
CROSSREFS
KEYWORD
nonn,tabf,base
AUTHOR
N. J. A. Sloane, Dec 30 2018
EXTENSIONS
More terms from Alois P. Heinz, Dec 30 2018
STATUS
approved