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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
Sequence in context: A325501 A007986 A013503 * A132481 A369680 A217652
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 13 09:39 EDT 2024. Contains 374274 sequences. (Running on oeis4.)