A367251 Lexicographically earliest sequence starting 1,2 which can be arranged in a mirror symmetric array shape such that a(n) is the length of the n-th row and no column has the same value more than once.

1, 2, 1, 2, 1, 2, 3, 3, 3, 1, 4, 1, 2, 5, 2, 3, 6, 3, 7, 1, 4, 4, 1, 8, 5, 5, 1, 4, 9, 4, 1, 6, 6, 5, 10, 5, 1, 2, 7, 7, 2, 1, 6, 11, 6, 1, 2, 7, 12, 7, 2, 1, 13, 3, 8, 8, 3, 4, 9, 9, 4, 14, 1, 2, 5, 10, 10, 5, 2, 1, 3, 8, 15, 8, 3, 4, 9, 16, 9, 4, 17, 6, 11, 11, 6, 1, 2, 5, 10, 18, 10

Offset: 1

Author

Neal Gersh Tolunsky, Nov 11 2023

Keywords

• nonn
• tabf

Comments

For row 5 onward, the row contents are mirror symmetric too (palindromes), as well as the shape.

Terms in the same column are successive positive integers (with some initial exceptions before row 5).

Examples

			Array (or "tree") begins, with mirror symmetry in row 5 and beyond:
  columns   v  v  v  v  v  v  v
  row 1:             1,
  row 2:          2,    1,
  row 3:             2,
  row 4:          1,    2,
  row 5:             3,
  row 6:          3,    3,
  row 7:       1,    4,    1,
  row 8:       2,    5,    2,
  row 9:       3,    6,    3,
  row 10:            7,
  row 11:   1,    4,    4,    1,
  row 12:            8,
  row 13:         5,    5,
		

Links

• Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000
• Thomas Scheuerle, blue: scatter plot of a(1) to a(10000); red: length of the row where a(n) is contained.
• Neal Gersh Tolunsky, First differences of first 100000 terms.
• Neal Gersh Tolunsky, Ordinal transform of first 100000 terms.
• Neal Gersh Tolunsky, Graph of first 100000 terms.

Crossrefs

Cf. A334081, A253028.

Programs

MATLAB

function a = A367251( max_n )
    a = [1 2 1 2 1 2];
    odd = zeros(1,max_n); even = odd;
    odd(1) = 2; even(1)= 2; c = 5;
    while  length(a) < max_n
        if mod(a(c),2) == 1
            odd(1:(a(c)+1)/2) = odd(1:(a(c)+1)/2)+1;
            a = [a odd((a(c)+1)/2:-1:2) odd(1:(a(c)+1)/2)];
        else
            even(1:a(c)/2) = even(1:a(c)/2)+1;
            a = [a even(a(c)/2:-1:1) even(1:a(c)/2)];
        end
        c = c + 1;
    end
end % Thomas Scheuerle, Nov 21 2023