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A322762
Irregular triangle read by rows: to get row n, take partitions of n ordered as in A080577, and in each partition, change each j-th occurrence of k to j; use compressed notation as in A322761.
2
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, 1, 11, 11, 112, 11, 111, 1123, 121, 112, 1112, 11234, 1231, 12123, 112345, 1234567, 1, 11, 11, 112, 11, 111, 1123, 12, 111
OFFSET
1,3
REFERENCES
D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.2.1.5, Problem 73, pp. 415, 761.
LINKS
EXAMPLE
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.
MAPLE
b:= (n, i)-> `if`(n=0 or i=1, [cat($1..n)], [(t->
seq(map(x-> cat($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(parse, b(n$2))[]:
seq(T(n), n=1..10); # Alois P. Heinz, Dec 30 2018
CROSSREFS
KEYWORD
nonn,tabf,look,base
AUTHOR
N. J. A. Sloane, Dec 30 2018
EXTENSIONS
More terms from Alois P. Heinz, Dec 30 2018
STATUS
approved