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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

Table of n, a(n) for n=0..6.

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.)