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 A322763 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 uncompressed notation as in A080577. 2
 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, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 3, 1, 2, 3, 1, 2, 1, 2, 1, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 3, 4, 1, 2, 3, 1, 1, 2, 1, 2, 3, 1, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 7 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A080577, A066633, A322761, A322763. Sequence in context: A026791 A080576 A321744 * A213211 A294775 A330461 Adjacent sequences:  A322760 A322761 A322762 * A322764 A322765 A322766 KEYWORD nonn,tabf,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 August 7 23:50 EDT 2022. Contains 355995 sequences. (Running on oeis4.)