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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 5 07:46 EDT 2020. Contains 335462 sequences. (Running on oeis4.)