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.

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

Author

N. J. A. Sloane, Dec 30 2018

Keywords

• nonn
• tabf
• look
• base

Examples

			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.
		

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..28, flattened

Crossrefs

Cf. A080577, A066633, A322761, A322763.

Programs

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

Extensions

More terms from Alois P. Heinz, Dec 30 2018