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

1,3

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

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

Cf. A080577, A066633, A322761, A322763.

Sequence in context: A334074 A010215 A059857 * A070649 A255864 A056583

Adjacent sequences: A322759 A322760 A322761 * A322763 A322764 A322765

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