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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.

%I A367251 #50 May 26 2024 08:21:05
%S A367251 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,
%T A367251 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,
%U A367251 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
%N 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.
%C A367251 For row 5 onward, the row contents are mirror symmetric too (palindromes), as well as the shape.
%C A367251 Terms in the same column are successive positive integers (with some initial exceptions before row 5).
%H A367251 Neal Gersh Tolunsky, <a href="/A367251/b367251.txt">Table of n, a(n) for n = 1..10000</a>
%H A367251 Thomas Scheuerle, <a href="/A367251/a367251.png">blue: scatter plot of a(1) to a(10000); red: length of the row where a(n) is contained</a>.
%H A367251 Neal Gersh Tolunsky, <a href="/A367251/a367251_5.png">First differences of first 100000 terms</a>.
%H A367251 Neal Gersh Tolunsky, <a href="/A367251/a367251_6.png">Ordinal transform of first 100000 terms</a>.
%H A367251 Neal Gersh Tolunsky, <a href="/A367251/a367251_7.png">Graph of first 100000 terms</a>.
%e A367251 Array (or "tree") begins, with mirror symmetry in row 5 and beyond:
%e A367251   columns   v  v  v  v  v  v  v
%e A367251   row 1:             1,
%e A367251   row 2:          2,    1,
%e A367251   row 3:             2,
%e A367251   row 4:          1,    2,
%e A367251   row 5:             3,
%e A367251   row 6:          3,    3,
%e A367251   row 7:       1,    4,    1,
%e A367251   row 8:       2,    5,    2,
%e A367251   row 9:       3,    6,    3,
%e A367251   row 10:            7,
%e A367251   row 11:   1,    4,    4,    1,
%e A367251   row 12:            8,
%e A367251   row 13:         5,    5,
%o A367251 (MATLAB)
%o A367251 function a = A367251( max_n )
%o A367251     a = [1 2 1 2 1 2];
%o A367251     odd = zeros(1,max_n); even = odd;
%o A367251     odd(1) = 2; even(1)= 2; c = 5;
%o A367251     while  length(a) < max_n
%o A367251         if mod(a(c),2) == 1
%o A367251             odd(1:(a(c)+1)/2) = odd(1:(a(c)+1)/2)+1;
%o A367251             a = [a odd((a(c)+1)/2:-1:2) odd(1:(a(c)+1)/2)];
%o A367251         else
%o A367251             even(1:a(c)/2) = even(1:a(c)/2)+1;
%o A367251             a = [a even(a(c)/2:-1:1) even(1:a(c)/2)];
%o A367251         end
%o A367251         c = c + 1;
%o A367251     end
%o A367251 end % _Thomas Scheuerle_, Nov 21 2023
%Y A367251 Cf. A334081, A253028.
%K A367251 nonn,tabf
%O A367251 1,2
%A A367251 _Neal Gersh Tolunsky_, Nov 11 2023