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 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. 2
 1, 1, 1, 1, 2, 12, 244 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS For n<=5, a(n) = A003121(n), but for n > 5, a(n) < A003121(n). 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. LINKS Vladimir Letsko, Mathematical Marathon, Problem 183 (in Russian) EXAMPLE Let a < b < c < d. There are two possible ways to arrange the sums in nondecreasing order: 1) a+b <= a+c <= a+d <= b+c <= b+d <= c+d, (for instance, a = 1, b = 3, c = 4, d = 5); 2) a+b <= a+c <= b+c <= a+d <= b+d <= c+d, (for instance, a = 1, b = 2, c = 3, d = 5). Hence a(4) = 2. CROSSREFS Cf. A231085, A003121, A237749. Sequence in context: A325501 A007986 A013503 * A132481 A217652 A320212 Adjacent sequences:  A231071 A231072 A231073 * A231075 A231076 A231077 KEYWORD nonn,more AUTHOR Vladimir Letsko, Nov 03 2013 EXTENSIONS Term a(0)=1 prepended by Max Alekseyev, Feb 23 2014 STATUS approved

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Last modified July 25 09:49 EDT 2021. Contains 346289 sequences. (Running on oeis4.)