cp's OEIS Frontend

A231074 The number of possible ways to arrange the sums x_i + x_j (1 <= i < j <= n) of the items x_1 < x_2 <...< x_n in nondecreasing order.

%I A231074 #18 Feb 23 2014 18:28:58
%S A231074 1,1,1,1,2,12,244
%N A231074 The number of possible ways to arrange the sums x_i + x_j (1 <= i < j <= n) of the items x_1 < x_2 <...< x_n in nondecreasing order.
%C A231074 For n<=5, a(n) = A003121(n), but for n > 5, a(n) < A003121(n).
%C A231074 Every possible ordering of sums provides a way of placing 1,2,...,n(n+1)/2 in a triangular array such that both rows and columns are increasing, but the reverse is generally not true.
%H A231074 Vladimir Letsko, <a href="http://www-old.fizmat.vspu.ru/doku.php?id=marathon:problem_183">Mathematical Marathon, Problem 183</a> (in Russian)
%e A231074 Let a < b < c < d. There are two possible ways to arrange the sums in nondecreasing order:
%e A231074 1) a+b <= a+c <= a+d <= b+c <= b+d <= c+d, (for instance, a = 1, b = 3, c = 4, d = 5);
%e A231074 2) a+b <= a+c <= b+c <= a+d <= b+d <= c+d, (for instance, a = 1, b = 2, c = 3, d = 5).
%e A231074 Hence a(4) = 2.
%Y A231074 Cf. A231085, A003121, A237749.
%K A231074 nonn,more
%O A231074 0,5
%A A231074 _Vladimir Letsko_, Nov 03 2013
%E A231074 Term a(0)=1 prepended by _Max Alekseyev_, Feb 23 2014