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

1,2

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).

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.

Example

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,

Prog

(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

Crossrefs

Cf. A334081, A253028.

Sequence in context: A249717 A249718 A244518 * A161310 A161244 A161029

Adjacent sequences: A367248 A367249 A367250 * A367252 A367253 A367254

Keyword

nonn,tabf

Author

Neal Gersh Tolunsky, Nov 11 2023

Status

approved