cp's OEIS Frontend

A319479 Lexicographically earliest sequence such that for every n and every sequence 1 <= b_1 < b_2 < ... < b_t = n, the values of barycenter((b_1, a(b_1)), (b_2, a(b_2)), ..., (b_t, a(b_t))) are distinct.

%I A319479 #19 Sep 23 2018 01:56:47
%S A319479 1,1,2,1,4,8,16,29,51,128,344,528,1863,5283,12445
%N A319479 Lexicographically earliest sequence such that for every n and every sequence 1 <= b_1 < b_2 < ... < b_t = n, the values of barycenter((b_1, a(b_1)), (b_2, a(b_2)), ..., (b_t, a(b_t))) are distinct.
%C A319479 The barycenter of the points {(x_1, y_1), (x_2, y_2), ..., (x_k, y_k)} is given by the average of the x and y coordinates: (Sum_{i=1..k} x_i/k, Sum_{i=1..k} y_i/k).
%e A319479 For n = 5, a(5) = 4 because letting a(5) = 1, 2, or 3 creates barycenter collisions:
%e A319479 +-----------+----------------+--------------------------------+------------+
%e A319479 | candidate | set 1          | set 2                          | barycenter |
%e A319479 +-----------+----------------+--------------------------------+------------+
%e A319479 | (5, 1)    | (1, 1); (5, 1) | (1, 1); (2, 1); (4, 1); (5, 1) | (6, 1)     |
%e A319479 | (5, 2)    | (2, 1); (5, 2) | (2, 1); (3, 2); (4, 1); (5, 2) | (3.5, 1.5) |
%e A319479 | (5, 3)    | (1, 1); (5, 3) | (1, 1); (3, 2); (5, 3)         | (3, 2)     |
%e A319479 +-----------+----------------+--------------------------------+------------+
%e A319479 And a(5) = 4 creates no such problems.
%Y A319479 Cf. A285491.
%K A319479 nonn,more
%O A319479 1,3
%A A319479 _Peter Kagey_, Sep 19 2018