A384034 Irregular triangle read by rows. Start with T(1,1) = 1. For each subsequent row, traverse the array so far. For each value m, insert m new values from the next unused integers immediately to the right of m. The process is repeated row by row, where each number in the array dictates how many new values are added after it.

1, 1, 2, 1, 3, 2, 4, 5, 1, 6, 3, 7, 8, 9, 2, 10, 11, 4, 12, 13, 14, 15, 5, 16, 17, 18, 19, 20, 1, 21, 6, 22, 23, 24, 25, 26, 27, 3, 28, 29, 30, 7, 31, 32, 33, 34, 35, 36, 37, 8, 38, 39, 40, 41, 42, 43, 44, 45, 9, 46, 47, 48, 49, 50, 51, 52, 53, 54, 2, 55, 56

Offset

1,3

Links

Table of n, a(n) for n=1..71.

Example

Triangle begins:
  1;
  1, 2;
  1, 3, 2, 4, 5;
  1, 6, 3, 7, 8, 9, 2, 10, 11, 4, 12, 13, 14, 15, 5, 16, 17, 18, 19, 20;
  ...
Row 1 = [1].
For m = 1, insert 1 new integer (next unused is 2) to the right of 1.
Row 2 = [1, 2].
For m = 1, insert 1 new integer (next unused is 3) to the right of 1.
For m = 2, insert 2 new integers (next unused are 4, 5) to the right of 2.
Row 3 = [1, 3, 2, 4, 5].
For m = 1, insert 1 new integer (6).
For m = 3, insert 3 new integers (7, 8, 9).
For m = 2, insert 2 new integers (10, 11).
For m = 4, insert 4 new integers (12, 13, 14, 15).
For m = 5, insert 5 new integers (16, 17, 18, 19, 20).
Row 4 = [1, 6, 3, 7, 8, 9, 2, 10, 11, 4, 12, 13, 14, 15, 5, 16, 17, 18, 19, 20].
And so on.

Crossrefs

Sequence in context: A174618 A365006 A144241 * A094173 A214370 A227859

Adjacent sequences: A384031 A384032 A384033 * A384035 A384036 A384037

Keyword

nonn,tabf

Author

Ali Sada, May 21 2025

Status

approved