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A231085 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 increasing order provided that all sums are different. 2
1, 1, 1, 1, 2, 12, 168, 4676 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

For n<=5, a(n) = A231074(n), but for n>5, a(n) < A231074(n). For instance, let n = 6 and a < b < c < d < e < f. Then the arrangement a+b <= a+c <= a+d <= a+e <= b+c <= b+d <= a+f <= b+e <= b+f <= c+d <= c+e <= c+f <= d+e <= d+f <= e+f is possible (e.g., for a = 1, b = 5, c = 9, d = 12, e=13, f = 16), while the same arrangement with "<" instead of "<=" is not possible.

LINKS

Table of n, a(n) for n=0..7.

Vladimir Letsko, Mathematical Marathon, Problem 183 (in Russian)

EXAMPLE

Let a < b < c < d. There are two possible ways to arrange the sums in increasing 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. A231074, A003121, A237749

Sequence in context: A052728 A052729 A098431 * A059522 A271857 A113149

Adjacent sequences:  A231082 A231083 A231084 * A231086 A231087 A231088

KEYWORD

nonn,more

AUTHOR

Vladimir Letsko, Nov 03 2013

EXTENSIONS

a(7) from Anton Nikonov, Feb 07 2014

Edited and a(0)=1 prepended by Max Alekseyev, Feb 19 2014

STATUS

approved

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Last modified February 22 22:35 EST 2020. Contains 332155 sequences. (Running on oeis4.)